{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 目标检测和边界框\n",
    "在前面的一些章节中，我们介绍了诸多用于图像分类的模型。在图像分类任务里，我们假设图像里只有一个主体目标，并关注如何识别该目标的类别。然而，很多时候图像里有多个我们感兴趣的目标，我们不仅想知道它们的类别，还想得到它们在图像中的具体位置。在计算机视觉里，我们将这类任务称为目标检测（object detection）或物体检测。\n",
    "\n",
    "目标检测在多个领域中被广泛使用。例如，在无人驾驶里，我们需要通过识别拍摄到的视频图像里的车辆、行人、道路和障碍的位置来规划行进线路。机器人也常通过该任务来检测感兴趣的目标。安防领域则需要检测异常目标，如歹徒或者炸弹。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from PIL import Image\n",
    "\n",
    "import sys\n",
    "sys.path.append(\"..\") \n",
    "import dl_utils"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
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       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\r\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\r\n",
       "<!-- Created with matplotlib (http://matplotlib.org/) -->\r\n",
       "<svg height=\"160.296562pt\" version=\"1.1\" viewBox=\"0 0 211.3875 160.296562\" width=\"211.3875pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\r\n",
       " <defs>\r\n",
       "  <style type=\"text/css\">\r\n",
       "*{stroke-linecap:butt;stroke-linejoin:round;}\r\n",
       "  </style>\r\n",
       " </defs>\r\n",
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       "   <path d=\"M 0 160.296562 \r\n",
       "L 211.3875 160.296562 \r\n",
       "L 211.3875 0 \r\n",
       "L 0 0 \r\n",
       "z\r\n",
       "\" style=\"fill:none;\"/>\r\n",
       "  </g>\r\n",
       "  <g id=\"axes_1\">\r\n",
       "   <g id=\"patch_2\">\r\n",
       "    <path d=\"M 33.2875 136.418437 \r\n",
       "L 200.6875 136.418437 \r\n",
       "L 200.6875 10.868437 \r\n",
       "L 33.2875 10.868437 \r\n",
       "z\r\n",
       "\" style=\"fill:#ffffff;\"/>\r\n",
       "   </g>\r\n",
       "   <g clip-path=\"url(#pdf6cfc0c60)\">\r\n",
       "    <image height=\"126\" id=\"imageda0b4b92ee\" transform=\"scale(1 -1)translate(0 -126)\" width=\"168\" x=\"33.2875\" xlink:href=\"data:image/png;base64,\r\n",
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      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dl_utils.set_figsize((3,6))\n",
    "zzfimg = Image.open('imgs/zzf.jpg')\n",
    "dl_utils.plt.imshow(zzfimg);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 不好意思搞错了\n",
    "应该是这个"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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\" y=\"-10.883422\"/>\r\n",
       "   </g>\r\n",
       "   <g id=\"matplotlib.axis_1\">\r\n",
       "    <g id=\"xtick_1\">\r\n",
       "     <g id=\"line2d_1\">\r\n",
       "      <defs>\r\n",
       "       <path d=\"M 0 0 \r\n",
       "L 0 3.5 \r\n",
       "\" id=\"m34c6e75515\" style=\"stroke:#000000;stroke-width:0.8;\"/>\r\n",
       "      </defs>\r\n",
       "      <g>\r\n",
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      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dl_utils.set_figsize((3,6))\n",
    "img = Image.open('imgs/catdog.jpg')\n",
    "dl_utils.plt.imshow(img);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 边界框\n",
    "在目标检测里，我们通常使用边界框（bounding box）来描述目标位置。边界框是一个矩形框，可以由矩形左上角的$x$和$y$轴坐标与右下角的$x$和$y$轴坐标确定。我们根据上面的图的坐标信息来定义图中狗和猫的边界框。图中的坐标原点在图像的左上角，原点往右和往下分别为$x$轴和$y$轴的正方向。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# bbox是bounding box的缩写\n",
    "dog_bbox, cat_bbox = [60, 45, 378, 516], [400, 112, 655, 493]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们可以在图中将边界框画出来，以检查其是否准确。画之前，我们定义一个辅助函数bbox_to_rect。它将边界框表示成matplotlib的边界框格式。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bbox_to_rect(bbox, color):  # 本函数已保存在d2lzh_pytorch中方便以后使用\n",
    "    # 将边界框(左上x, 左上y, 右下x, 右下y)格式转换成matplotlib格式：\n",
    "    # ((左上x, 左上y), 宽, 高)\n",
    "    return dl_utils.plt.Rectangle(\n",
    "        xy=(bbox[0], bbox[1]), width=bbox[2]-bbox[0], height=bbox[3]-bbox[1],\n",
    "        fill=False, edgecolor=color, linewidth=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
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       "  <clipPath id=\"pd441190205\">\r\n",
       "   <rect height=\"128.999176\" width=\"167.4\" x=\"33.2875\" y=\"10.884246\"/>\r\n",
       "  </clipPath>\r\n",
       " </defs>\r\n",
       "</svg>\r\n"
      ],
      "text/plain": [
       "<Figure size 216x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#我们将边界框加载在图像上，可以看到目标的主要轮廓基本在框内。\n",
    "\n",
    "fig = dl_utils.plt.imshow(img)\n",
    "fig.axes.add_patch(bbox_to_rect(dog_bbox, 'blue'))\n",
    "fig.axes.add_patch(bbox_to_rect(cat_bbox, 'red'));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 在目标检测里不仅需要找出图像里面所有感兴趣的目标，而且要知道它们的位置。位置一般由矩形边界框来表示。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.patches.Rectangle at 0x1d9113552e8>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\r\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\r\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\r\n",
       "<!-- Created with matplotlib (http://matplotlib.org/) -->\r\n",
       "<svg height=\"160.296562pt\" version=\"1.1\" viewBox=\"0 0 211.3875 160.296562\" width=\"211.3875pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\r\n",
       " <defs>\r\n",
       "  <style type=\"text/css\">\r\n",
       "*{stroke-linecap:butt;stroke-linejoin:round;}\r\n",
       "  </style>\r\n",
       " </defs>\r\n",
       " <g id=\"figure_1\">\r\n",
       "  <g id=\"patch_1\">\r\n",
       "   <path d=\"M 0 160.296562 \r\n",
       "L 211.3875 160.296562 \r\n",
       "L 211.3875 0 \r\n",
       "L 0 0 \r\n",
       "z\r\n",
       "\" style=\"fill:none;\"/>\r\n",
       "  </g>\r\n",
       "  <g id=\"axes_1\">\r\n",
       "   <g id=\"patch_2\">\r\n",
       "    <path d=\"M 33.2875 136.418437 \r\n",
       "L 200.6875 136.418437 \r\n",
       "L 200.6875 10.868437 \r\n",
       "L 33.2875 10.868437 \r\n",
       "z\r\n",
       "\" style=\"fill:#ffffff;\"/>\r\n",
       "   </g>\r\n",
       "   <g clip-path=\"url(#p43f5afd5b6)\">\r\n",
       "    <image height=\"126\" id=\"image6bdd4d779d\" transform=\"scale(1 -1)translate(0 -126)\" width=\"168\" x=\"33.2875\" xlink:href=\"data:image/png;base64,\r\n",
       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     "metadata": {
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     "output_type": "display_data"
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   ],
   "source": [
    "fig = dl_utils.plt.imshow(zzfimg)\n",
    "zzf_bbox = [50,35,600,470]\n",
    "fig.axes.add_patch(bbox_to_rect(zzf_bbox, 'blue'))"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 锚框 Anchor\n",
    "目标检测算法通常会在输入图像中采样大量的区域，然后判断这些区域中是否包含我们感兴趣的目标，并调整区域边缘从而更准确地预测目标的真实边界框（ground-truth bounding box）。不同的模型使用的区域采样方法可能不同。这里我们介绍其中的一种方法：**它以每个像素为中心** 生成**多个大小和宽高比（aspect ratio）不同的边界框**。这些边界框被称为**锚框（anchor box）**。我们将在后面基于锚框实践目标检测。"
   ]
  },
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   "metadata": {},
   "source": [
    "\n",
    "\n",
    "### 每个像素为中心，生成若干宽高比的锚框 生成多个锚框\n",
    "\n",
    "假设输入图像高为$h$，宽为$w$。我们分别以图像的每个像素为中心生成不同形状的锚框。设大小为$s\\in (0,1]$且宽高比为$r > 0$，那么锚框的宽和高将分别为$ws\\sqrt{r}$和$hs/\\sqrt{r}$。当中心位置给定时，已知宽和高的锚框是确定的。\n",
    "\n",
    "下面我们分别设定好一组大小$s_1,\\ldots,s_n$和一组宽高比$r_1,\\ldots,r_m$。如果以每个像素为中心时使用所有的大小与宽高比的组合，输入图像将一共得到$whnm$个锚框。虽然这些锚框可能覆盖了所有的真实边界框，但计算复杂度容易过高。因此，我们通常只对包含$s_1$或$r_1$的大小与宽高比的组合感兴趣，即\n",
    "\n",
    "$$(s_1, r_1), (s_1, r_2), \\ldots, (s_1, r_m), (s_2, r_1), (s_3, r_1), \\ldots, (s_n, r_1).$$\n",
    "\n",
    "也就是说，以相同像素为中心的锚框的数量为$n+m-1$。对于整个输入图像，我们将一共生成$wh(n+m-1)$个锚框。\n",
    "\n",
    "以上生成锚框的方法实现在下面的MultiBoxPrior函数中。指定输入、一组大小和一组宽高比，该函数将返回输入的所有锚框。\n",
    "\n",
    "注: PyTorch官方在torchvision.models.detection.rpn里有一个AnchorGenerator类可以用来生成anchor，但是和这里讲的不一样，感兴趣的可以去看看。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w = 728, h = 561\n",
      "[[0.75       1.        ]\n",
      " [0.75       1.41421356]\n",
      " [0.75       0.70710678]\n",
      " [0.5        1.        ]\n",
      " [0.25       1.        ]]\n",
      "[0.75       1.06066017 0.53033009 0.5        0.25      ] [0.75       0.53033009 1.06066017 0.5        0.25      ]\n",
      "[0.75 0.75 0.75 0.5  0.25]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 2042040, 4])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dl_utils.set_figsize()\n",
    "img = Image.open('imgs/catdog.jpg')\n",
    "w, h = img.size\n",
    "import torch\n",
    "import math\n",
    "import numpy as np\n",
    "print(\"w = %d, h = %d\" % (w, h)) # w = 728, h = 561\n",
    "# 本函数已保存在d2lzh_pytorch包中方便以后使用\n",
    "# size 是归一化大小， 例如size = 0.5 对应面积为 0.5*0.5, 比例为1的的bbox\n",
    "def MultiBoxPrior(feature_map, sizes=[0.75, 0.5, 0.25], ratios=[1, 2, 0.5]):\n",
    "    \"\"\"\n",
    "    # 按照「9.4.1. 生成多个锚框」所讲的实现, anchor表示成(xmin, ymin, xmax, ymax).\n",
    "    https://zh.d2l.ai/chapter_computer-vision/anchor.html\n",
    "    Args:\n",
    "        feature_map: torch tensor, Shape: [N, C, H, W].\n",
    "        sizes: List of sizes (0~1) of generated MultiBoxPriores. \n",
    "        ratios: List of aspect ratios (non-negative) of generated MultiBoxPriores. \n",
    "    Returns:\n",
    "        anchors of shape (1, num_anchors, 4). 由于batch里每个都一样, 所以第一维为1\n",
    "    \"\"\"\n",
    "    #全部覆盖复杂度高，只覆盖部分大小和宽高比。\n",
    "    pairs = [] # pair of (size, sqrt(ration))\n",
    "    for r in ratios:\n",
    "        pairs.append([sizes[0], math.sqrt(r)])\n",
    "    for s in sizes[1:]:\n",
    "        pairs.append([s, math.sqrt(ratios[0])])\n",
    "    \n",
    "    pairs = np.array(pairs)\n",
    "    print(pairs)\n",
    "    \n",
    "    ss1 = pairs[:, 0] * pairs[:, 1] # size * sqrt(ration)\n",
    "    ss2 = pairs[:, 0] / pairs[:, 1] # size / sqrt(ration)\n",
    "    print(ss1,ss2)\n",
    "    print(np.sqrt(ss1*ss2))\n",
    "    base_anchors = np.stack([-ss1, -ss2, ss1, ss2], axis=1) / 2\n",
    "    \n",
    "    h, w = feature_map.shape[-2:]\n",
    "    shifts_x = np.arange(0, w) / w\n",
    "    shifts_y = np.arange(0, h) / h\n",
    "    shift_x, shift_y = np.meshgrid(shifts_x, shifts_y)\n",
    "    shift_x = shift_x.reshape(-1)\n",
    "    shift_y = shift_y.reshape(-1)\n",
    "    shifts = np.stack((shift_x, shift_y, shift_x, shift_y), axis=1)\n",
    "    \n",
    "    anchors = shifts.reshape((-1, 1, 4)) + base_anchors.reshape((1, -1, 4))\n",
    "    \n",
    "    return torch.tensor(anchors, dtype=torch.float32).view(1, -1, 4)\n",
    "\n",
    "\n",
    "X = torch.Tensor(1, 3, h, w)  # 构造输入数据\n",
    "Y = MultiBoxPrior(X, sizes=[0.75, 0.5, 0.25], ratios=[1, 2, 0.5])\n",
    "Y.shape # torch.Size([1, 2042040, 4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们看到，返回锚框变量y的形状为（1，锚框个数，4）。将锚框变量y的形状变为（图像高，图像宽，以相同像素为中心的锚框个数，4）后，我们就可以通过指定像素位置来获取所有以该像素为中心的锚框了。下面的例子里我们访问以（250，250）为中心的第一个锚框。它有4个元素，分别是锚框左上角的$x$和$y$轴坐标和右下角的$x$和$y$轴坐标，其中$x$和$y$轴的坐标值分别已除以图像的宽和高，因此值域均为0和1之间。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([-0.0316,  0.0706,  0.7184,  0.8206])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boxes = Y.reshape((h, w, 5, 4))\n",
    "boxes[250, 250, 0, :]# * torch.tensor([w, h, w, h], dtype=torch.float32)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以验证一下以上输出对不对：size和ratio分别为0.75和1, 则(归一化后的)宽高均为0.75, 所以输出是正确的（0.75 = 0.7184 + 0.0316 = 0.8206 - 0.0706）。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "#为了描绘图像中以某个像素为中心的所有锚框，我们先定义show_bboxes函数以便在图像上画出多个边界框。\n",
    "\n",
    "# 本函数已保存在d2lzh_pytorch包中方便以后使用\n",
    "def show_bboxes(axes, bboxes, labels=None, colors=None):\n",
    "    def _make_list(obj, default_values=None):\n",
    "        if obj is None:\n",
    "            obj = default_values\n",
    "        elif not isinstance(obj, (list, tuple)):\n",
    "            obj = [obj]\n",
    "        return obj\n",
    "\n",
    "    labels = _make_list(labels)\n",
    "    colors = _make_list(colors, ['b', 'g', 'r', 'm', 'c'])\n",
    "    for i, bbox in enumerate(bboxes):\n",
    "        color = colors[i % len(colors)]\n",
    "        rect = dl_utils.bbox_to_rect(bbox.detach().cpu().numpy(), color)\n",
    "        axes.add_patch(rect)\n",
    "        if labels and len(labels) > i:\n",
    "            text_color = 'k' if color == 'w' else 'w'\n",
    "            axes.text(rect.xy[0], rect.xy[1], labels[i],\n",
    "                      va='center', ha='center', fontsize=6, color=text_color,\n",
    "                      bbox=dict(facecolor=color, lw=0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "刚刚我们看到，变量boxes中$x$和$y$轴的坐标值分别已除以图像的宽和高。在绘图时，我们需要恢复锚框的原始坐标值，并因此定义了变量bbox_scale。现在，我们可以画出图像中以(250, 250)为中心的所有锚框了。可以看到，大小为0.75且宽高比为1的锚框较好地覆盖了图像中的狗。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<module 'dl_utils' from '..\\\\dl_utils.py'>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from imp import reload\n",
    "reload(dl_utils)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 252x180 with 1 Axes>"
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   ],
   "source": [
    "dl_utils.set_figsize()\n",
    "fig = dl_utils.plt.imshow(img)\n",
    "bbox_scale = torch.tensor([[w, h, w, h]], dtype=torch.float32)\n",
    "show_bboxes(fig.axes, boxes[250, 250, :, :] * bbox_scale,\n",
    "            ['s=0.75, r=1', 's=0.75, r=2', 's=0.55, r=0.5', 's=0.5, r=1', 's=0.25, r=1'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([5, 4])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boxes[250, 250, :, :].shape"
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ## 交并比\n",
    "我们刚刚提到某个锚框较好地覆盖了图像中的狗。如果该目标的真实边界框已知，这里的“较好”该如何量化呢？一种直观的方法是衡量锚框和真实边界框之间的相似度。我们知道，Jaccard系数（Jaccard index）可以衡量两个集合的相似度。给定集合$\\mathcal{A}$和$\\mathcal{B}$，它们的Jaccard系数即二者交集大小除以二者并集大小：\n",
    "\n",
    "$$J(\\mathcal{A},\\mathcal{B}) = \\frac{\\left|\\mathcal{A} \\cap \\mathcal{B}\\right|}{\\left| \\mathcal{A} \\cup \\mathcal{B}\\right|}.$$\n",
    "\n",
    "实际上，我们可以把边界框内的像素区域看成是像素的集合。如此一来，我们可以用两个边界框的像素集合的Jaccard系数衡量这两个边界框的相似度。当衡量两个边界框的相似度时，我们通常将Jaccard系数称为交并比（Intersection over Union，IoU），即两个边界框相交面积与相并面积之比，如图9.2所示。交并比的取值范围在0和1之间：0表示两个边界框无重合像素，1表示两个边界框相等。\n",
    "<div align=center>\n",
    "<img width=\"400\" src=\"imgs/9.4_iou.svg\"/>\n",
    "</div>\n",
    "<div align=center> 交并比是两个边界框相交面积与相并面积之比</div>\n",
    "![]()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 以下函数已保存在d2lzh_pytorch包中方便以后使用\n",
    "# 参考https://github.com/sgrvinod/a-PyTorch-Tutorial-to-Object-Detection/blob/master/utils.py#L356\n",
    "def compute_intersection(set_1, set_2):\n",
    "    \"\"\"\n",
    "    计算anchor之间的交集\n",
    "    Args:\n",
    "        set_1: a tensor of dimensions (n1, 4), anchor表示成(xmin, ymin, xmax, ymax)\n",
    "        set_2: a tensor of dimensions (n2, 4), anchor表示成(xmin, ymin, xmax, ymax)\n",
    "    Returns:\n",
    "        intersection of each of the boxes in set 1 with respect to each of the boxes in set 2, shape: (n1, n2)\n",
    "    \"\"\"\n",
    "    # PyTorch auto-broadcasts singleton dimensions\n",
    "    lower_bounds = torch.max(set_1[:, :2].unsqueeze(1), set_2[:, :2].unsqueeze(0))  # (n1, n2, 2)\n",
    "    upper_bounds = torch.min(set_1[:, 2:].unsqueeze(1), set_2[:, 2:].unsqueeze(0))  # (n1, n2, 2)\n",
    "    intersection_dims = torch.clamp(upper_bounds - lower_bounds, min=0)  # (n1, n2, 2)\n",
    "    return intersection_dims[:, :, 0] * intersection_dims[:, :, 1]  # (n1, n2)\n",
    "\n",
    "\n",
    "def compute_jaccard(set_1, set_2):\n",
    "    \"\"\"\n",
    "    计算anchor之间的Jaccard系数(IoU)\n",
    "    Args:\n",
    "        set_1: a tensor of dimensions (n1, 4), anchor表示成(xmin, ymin, xmax, ymax)\n",
    "        set_2: a tensor of dimensions (n2, 4), anchor表示成(xmin, ymin, xmax, ymax)\n",
    "    Returns:\n",
    "        Jaccard Overlap of each of the boxes in set 1 with respect to each of the boxes in set 2, shape: (n1, n2)\n",
    "    \"\"\"\n",
    "    # Find intersections\n",
    "    intersection = compute_intersection(set_1, set_2)  # (n1, n2)\n",
    "\n",
    "    # Find areas of each box in both sets\n",
    "    areas_set_1 = (set_1[:, 2] - set_1[:, 0]) * (set_1[:, 3] - set_1[:, 1])  # (n1)\n",
    "    areas_set_2 = (set_2[:, 2] - set_2[:, 0]) * (set_2[:, 3] - set_2[:, 1])  # (n2)\n",
    "\n",
    "    # Find the union\n",
    "    # PyTorch auto-broadcasts singleton dimensions\n",
    "    union = areas_set_1.unsqueeze(1) + areas_set_2.unsqueeze(0) - intersection  # (n1, n2)\n",
    "\n",
    "    return intersection / union  # (n1, n2)"
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   "source": [
    "## 标注训练集的锚框\n",
    "在训练集中，我们将每个锚框视为一个训练样本。为了训练**目标检测模型**，我们需要为**每个锚框标注两类标签**：一是锚框所含**目标的类别，简称类别**；二是**真实边界框相对锚框的偏移量，简称偏移量（offset）**。在目标检测时，我们首先**生成多个锚框**，然后为每个锚框**预测类别以及偏移量**，接着根据**预测的偏移量调整锚框位置**从而得到预测边界框，最后筛选需要输出的预测边界框。\n",
    "\n",
    "我们知道，在目标检测的训练集中，每个图像已标注了**真实边界框的位置**以及所含**目标的类别**。在生成锚框之后，我们主要依据与锚框相似的真实边界框的位置和类别信息为锚框标注。那么，该如何为锚框分配与其相似的真实边界框呢？\n",
    "\n",
    "假设图像中锚框分别为$A_1, A_2, \\ldots, A_{n_a}$，真实边界框分别为$B_1, B_2, \\ldots, B_{n_b}$，且$n_a \\geq n_b$。定义矩阵$\\boldsymbol{X} \\in \\mathbb{R}^{n_a \\times n_b}$，其中第$i$行第$j$列的元素$x_{ij}$为锚框$A_i$与真实边界框$B_j$的交并比。 首先，我们找出矩阵$\\boldsymbol{X}$中最大元素，并将该元素的行索引与列索引分别记为$i_1,j_1$。我们为锚框$A_{i_1}$分配真实边界框$B_{j_1}$。显然，锚框$A_{i_1}$和真实边界框$B_{j_1}$在所有的“锚框—真实边界框”的配对中相似度最高。接下来，将矩阵$\\boldsymbol{X}$中第$i_1$行和第$j_1$列上的所有元素丢弃。找出矩阵$\\boldsymbol{X}$中剩余的最大元素，并将该元素的行索引与列索引分别记为$i_2,j_2$。我们为锚框$A_{i_2}$分配真实边界框$B_{j_2}$，再将矩阵$\\boldsymbol{X}$中第$i_2$行和第$j_2$列上的所有元素丢弃。此时矩阵$\\boldsymbol{X}$中已有两行两列的元素被丢弃。 依此类推，直到矩阵$\\boldsymbol{X}$中所有$n_b$列元素全部被丢弃。这个时候，我们已为$n_b$个锚框各分配了一个真实边界框。 接下来，我们只遍历剩余的$n_a - n_b$个锚框：给定其中的锚框$A_i$，根据矩阵$\\boldsymbol{X}$的第$i$行找到与$A_i$交并比最大的真实边界框$B_j$，且只有当该交并比大于预先设定的阈值时，才为锚框$A_i$分配真实边界框$B_j$。\n",
    "\n",
    "如图9.3（左）所示，假设矩阵$\\boldsymbol{X}$中最大值为$x_{23}$，我们将为锚框$A_2$分配真实边界框$B_3$。然后，丢弃矩阵中第2行和第3列的所有元素，找出剩余阴影部分的最大元素$x_{71}$，为锚框$A_7$分配真实边界框$B_1$。接着如图9.3（中）所示，丢弃矩阵中第7行和第1列的所有元素，找出剩余阴影部分的最大元素$x_{54}$，为锚框$A_5$分配真实边界框$B_4$。最后如图9.3（右）所示，丢弃矩阵中第5行和第4列的所有元素，找出剩余阴影部分的最大元素$x_{92}$，为锚框$A_9$分配真实边界框$B_2$。之后，我们只需遍历除去$A_2, A_5, A_7, A_9$的剩余锚框，并根据阈值判断是否为剩余锚框分配真实边界框。\n",
    "<div align=center>\n",
    "<img width=\"400\" src=\"imgs/9.4_anchor-label.svg\"/>\n",
    "</div>\n",
    "<div align=center> 锚框分配真实边界框</div>\n",
    "现在我们可以标注锚框的类别和偏移量了。如果一个锚框$A$被分配了真实边界框$B$，将锚框$A$的类别设为$B$的类别，并根据$B$和$A$的中心坐标的相对位置以及两个框的相对大小为锚框$A$标注偏移量。由于数据集中各个框的位置和大小各异，因此这些相对位置和相对大小通常需要一些特殊变换，才能使偏移量的分布更均匀从而更容易拟合。设锚框$A$及其被分配的真实边界框$B$的中心坐标分别为$(x_a, y_a)$和$(x_b, y_b)$，$A$和$B$的宽分别为$w_a$和$w_b$，高分别为$h_a$和$h_b$，一个常用的技巧是将$A$的偏移量标注为\n",
    "\n",
    "$$ \\left( \\frac{ \\frac{x_b - x_a}{w_a} - \\mu_x }{\\sigma_x}, \\frac{ \\frac{y_b - y_a}{h_a} - \\mu_y }{\\sigma_y}, \\frac{ \\log \\frac{w_b}{w_a} - \\mu_w }{\\sigma_w}, \\frac{ \\log \\frac{h_b}{h_a} - \\mu_h }{\\sigma_h}\\right), $$\n",
    "\n",
    "其中常数的默认值为$\\mu_x = \\mu_y = \\mu_w = \\mu_h = 0, \\sigma_x=\\sigma_y=0.1, \\sigma_w=\\sigma_h=0.2$。如果一个锚框没有被分配真实边界框，我们只需将该锚框的类别设为背景。类别为背景的锚框通常被称为负类锚框，其余则被称为正类锚框。\n",
    "\n",
    "下面演示一个具体的例子。我们为读取的图像中的猫和狗定义真实边界框，其中第一个元素为类别（0为狗，1为猫），剩余4个元素分别为左上角的$x$和$y$轴坐标以及右下角的$x$和$y$轴坐标（值域在0到1之间）。这里通过左上角和右下角的坐标构造了5个需要标注的锚框，分别记为$A_0, \\ldots, A_4$（程序中索引从0开始）。先画出这些锚框与真实边界框在图像中的位置。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
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3iVot4jimwmM8zlkcTTi32uU9j2xw6dwGcaH5/X/zGdIy5sxgi+e+cZvx0ZDNlT6XHzvP4cGMb77wGi8++wK/+AtPUfuNF0bcT2of1Js0g7Z+yNNq+XACbEhFre7vM4T9LarEB2eyd8K+d08sbFpnr7A72qEoCtzQPZ12s7xAKUWS57imRKmGvDdNswGKbbOYK4ajIUvdFkrVpxfK933qomZ6eIgTJ00hQmdEQUCtcmoh6EQmWXJAPJtgyRxUShzDPPY4mCh+/X/8JNq+yNKlZTY3QyLboa5rHMemdgVFltNdatNxJdJoPMoJkI+SmqKouHdvj9FowuHeHQyrGQSm7RBK/6Gbin0/ZjRNE8eysSzr+AYrdF0Q793mV37+vRze3SMMQxaLBd2lLoYXYAYhnaU1Pv+Vl7lw8TEMpbl95wZ/+2/950ynUyTg+z7Ly8uUQJZl/PZv/zbnzl2g3++TZRme13jqZ7/5IlEU4VDQshUb6yt89S/+nKW1LeLJERgmo/mYtZU2K72A/Z3buFZFlmruvPoCq/2I8eEB7mCDNJ5TFdn9AWkYTV4gZVO4qQXCvA8bw24KMqo6rtBWgrKucRwHIUEYClXVuK5LlhdIqwnfhBBN1fY7UHvfjX3PxY7qeDt97fMYRy+TFNXpieRFRZ4liLrEUCVpmuN5HpZlUZYl2WJCVebk8QzqAimaGPJkCi/LEomgVg3gHcuiRGGHfjPiqxJpGJRJRrFYEHotJkbIr/73/zvaWafdXmNlJSSwJUJoOq0A6gLXgvksIc9LRqMReZ7jSMHy8jJFUWCaJolqNMl5nlMUBbW2meUlozRjkiQYyjodrFJKpKFPb7RpmhjHN8YwDAwq1gLFo0su77m8ymI2b0IUz+Ty45cx3S6VENhBwDy1mVQuZZGwd/c268t9Vi//JPPJhBuvvkSRxpy9dIXAb/Hp3/9DPvzhj3Du0bP0ej0A7ty5A/Pb3Lp+jz/77L+j3fbwhcF6P6JUJr2Vbf7kTz/Hhz/2k8yO9qFQ/MSHP4AwSm69vse1l2/y8Y9/jNZSn7EIMV0f22oG5omc9SHhlOE8xAnndYkQgqJoEuO64lQKa9s2pnTxPA+Aoq4wfbe5FpaFbdvvCIi/98QOhYFBu3eO4fQG0rBQVYEATNNAuA7xNEXoCiFBC0VdpQhVImVFkWaY0qAsoFAFvu+faod930eaJqJsABXHMRiCLMuwbZu8zGhbBkfDGZ7f5vao5u//r/8Ev3eZC1sb2K6iHdq4MiLwPdAlRTqjGwRUSYLKC3qRQ+kaVEWGpKDbcpvYr9LUNbTckNHRBByJMBRSWIRWwCitWGQ5RV6hpYkWxrFHyTAQuEKgVYFlSlqupNcfMGi5mCim0wlJYuMHDnWekWaHBK0IkdeYacrVjasErssta05ndYOxVbJxZoV2q8UL33gOU5tMDsd8+Cd/nFanRVak5HlON3TJ5zu0qxFGMWGl36fd8dBJTJIVKEpuvv4KVV3zyksv0w8DOlGLr3/laZZW+1y9epUn3v8e0qzkcDwh0yk1EtM0TpNew7FOQayUwhAWWZZR5hXj8Zg7e7fYv7vP7d0d7h4eEsc5dVlx4cwm9+7d4z3veR97u0doJTEMuHLlLO953/v5qY9+jKW1ZRw/AEBjfJvo+vsEYgOFwMC0fLRpIIoT1rtCICjzFMcSlEWNYQgW8wmONKjzBNMSFHmCI00sQzCeLhgdDun1eiRxgmVITK/pypBCkmUZWmt836eIU+p8SiIlZaE5SjL+0Sc+Q7B0jotnztB1od1tnU7pkR9AVaJsyfToAM8yEa7NrMjwAw8R+gRBQFEU+K5LHi/wQ5/ZNKHTbjNPF4S2CUojqorCNjENSWqU1AqKWlFXFYYpsKSJbQhMy8J3JMudNqFr0e92mI4nVEVBVWScO3OZ8eEBrU6Pyd4cx3HY3d1ld+celi5RwkDYgmw+xYwGVJXHx3/+Kco8YXd/iGF7hO0O0jUIDMkX//QzqGQfqx00xQet8d2Adm+Jw8NDLMOgqnOWuxFdxyIwBUl8xLkLFwg7LW7uvI7lhNhOwHxRsHu4g2E24A2CANd1wbzvieu6pq5EwwZVFUVRYKgalef0ojZxVWHVU9qDgPVel5/6sfcxGo+5uPUkZVHz7LPPsr26hG1o9nbuIG2DrmHguAEKeKsk3FsvOx+3AJkKbGlSZRlpFmNJgbQtkukRfhgiTEmdJ1R5Sp7miLpkMZ9iGybdTofxeIyqayzTJF4sSJOEKIoYTSa0A4/JZML0aES320XFCcMCcmeZf/zPPo1cfpwrFx7BMyoCF4SqsaUDaOLpCKqKyLPJFnMcW2IJ8G0LVVe0222qqqQd+MxmM1pRSFGUdNoRSZLhmIJFmuGaJsJ3KOMSE40b+iziFMcyEEJSVCWh7xBYBo5pInVF5JqoMiNbLDA1eKZJ1AqIpyNUaVMs5iwtLZGNZ9TzMSU5g7U+pm2DmuEt5viOpqodJoeaqipYX1nD8TpIy0ORc/255xDxGLIRsZTUlcAyXW7dvMd7n3yCIOrT7/fZ3txicrSLqGtm0yOCpYhS12gJrt/iYH/G3Z3ruF6EdBzSeEKtKhZTG9/3wbyf0CqlkMYDiZpW7N65i6g0g26PL3ztq3zoypPoomC1FbHSitBJzJmVPnv7uzyyvUwrdMkWM5LFBK23T1WNygAp3lpY8dZBLAS2aUFeMh9PoCpwPRNVF0yGRwSOSbqY49om0zTGNiGZx5RZTrqI0VWN54bURYESkrIokFIyX8wo4pQwDElmc3RZ4ZoWh7t7SCGJRYtPf+4ZVi/+BCv9HkotGPS7uK6LKyVpmlKWJZ5pEydzTK/H6soSo6NDHBPiMm1oNalxTBND1Ax6LRKlUIXCNDRpXeBKiQw9FmlBmmWEtofIC0qt0bZEWk1snGU1Z7dWKOZzbFOgK4VjlLQij727O6z1BywPBgShRVXldNoBduAS53PCdsj5/llu3D1gejRmdW0DQ0FR54z2btDp9ZncvY7f6qBlTJX1KLTD3p0Xufb8a6yuLCPdFcDk6GhIp73E4dGQO/eOME2Trz39eR577BJ1kdDvtQkcE8NyWV9ZZ/9gxuc+/1WypCDPczx/TiUUgWMjhG4KHrmPYTWxseM4TdIq77MT8XzOnVu3sWqTgWFgYrA/2ufs1ia1odgfjfjmyzd4749/GKcd0Fnqs7GyghuGdHsdRsMD+iurbxmCbwPEJpoKLWK0DEEPsSyLWlVMxxNcz6Lb7TKfjTBlzcH+AYNuhzROkEKjDPBsi0opdu7eot1u47kWo6MDBpvnKFRMHidMF3NECqqu8GwLlGJaFPze0zcJB5tEnsY1C7rdHo7rEoYReZyw1O0jDY2gIvIlnmViGBXu3MCUBqsrS3iexyKLsR2PoiiRhoOoYzxHIg1J7Tv4vsvBcExpgHAdsqpCoim1IHJsEBrP8xCdgLZjssgEEo02LYTWhIEHymVSpGR7c7Y3epQkGEYHW0jsKKJCYwUeTzx2nqqqmM4XOKaNE/bQWqCVQcvrIEWEjYkpKl557Rp5PWP7/AadziqG6fKlP/s8ta4o8gLXdanRLCYjrl6+iONIJmnNaDQi3FhCem1wWvzrz3yKRZzhWC6ua2O5DpYhqMv8ONEyKMsazzRxTAvnuBhUmxbStJiNFrzwQlOMOtw/ZJHEXNjaJEkaB9Xv9rh9+zZ1XfPJT36Kn/mZj1JXBkUN6+1ek9xjoooSkEjTeMvxxFvyxAoDwzCxrDaVnGC7HqVW9Pw+qi6oshQpJXma4jgWi8UCUwsEkjwrqbKCyXDEoN9HCMFoOGTQ78NixIX1PsPhEK0NCrlAmwG15XN7Z48Xr+dEa4/Q9i1c0SSFpmkiDYM8zcjSZl+lCooKbCcg6IQYsUXoGVjS4LXXXgMsDAl1XbK0tMR0EuM6NlpBWSpsU6JVRRD4aFkQmRZ5VjbaCS3Jqxoh9Gn2TpkQuhZHR0dEUYRSNXEc03MsksUMv9PG9Uy6rT6OY2OYEsv16C8tkymB9NqYQuCtCeI4RugUP+xhOBGWFVELA8O2SZOYs+c2UOYFkrjk1VducfvWDoblkM5j9vb2kJbDeDJpZp1kjsAn9Cz6S13a/Q7dpQGf/dwXmMcLbMujKDKiKCDPc5aWlqhLm7oucRyHbreL53l4nnfKVpSGgWla/MG//RPyrKDdadHrdzk82Mf3fTYuPIKoK/Z27rGYTLj86Dq7u7sYOuGzn/3/+LEPfRBV5ayurmKbb5+ZeAsgPqnWGAhcTBlQGhbCNDBtRZYeIbjf0vNgm0yapuzeO8AQApWXBH6LLC0bOquuMUSCKQXZwZSktGn3l3j9pX1u7h4xr2LSSlJZLXSSMGj1sMxjDrUsm9jcsgi7bYJ2C2kqLOniOzbx4oAoknhRh7IouPjoBY6OjpCuTZFXlGXZ0D2eQ1lULBYT0AZCNNJFZZgUVY0lFEKKBmyuRxzHGKrGNiWoRtDeCX20qtDUZHmJ5QqWI5de2wMU88UYL/Axgw7C8VGWj+93kOEaVAUqX+BjMZ+kzMdzemsrxLWNG3jUSuMFAXt3d/jqXzaqtY31LUzT5rN/9nmCICCKIqIoQmuNKWoWiwWBa9NfamO5Dtpxubd3wHQ6xXVdlvrL1Flz/W3bxLVstGViGOA4Dq7rIh2PQoGUFhUC13UxDElRNGFIPB3R6XTwbQlVTpqm7O/c5ckrl/B9l/lsyNpqjyi0eerjH2E+n2OImrQqaHlBQ+GZZlMc+sGA+AGzAqKoTz69TZrPmoqVaVMXMcPhkFbk3U8GRLPtdgcc7O0TeSFlkmGZEkM0ZV/P8/jzazvc2rnLvDawvUPSRXasdQBpGwRG2QwhoVk/8whLS0tUVcXKygoIA+m4GAYs4jHM5oh0Qd+tqKqEw4MJlumxu7tDFEVITCzToSwVpmlSFBmq1rTbbeazuBmyx32AwpA4tsRGoowmFGoHXkM1pTFKV+i6Oi5bN+Q/huDc9hbDO68wGQ8JOit0uhGmaZCWGa1On1o6SBlSlBpbQ5VlHO3eAStgNC35nT/+PRLl0llqc/WRSyTDMTotKJXkYG9GK0rJsoQrjz/JM888g2V7WE7JYjblyccvMRka+L6LH9gEgx5up88z33gOrTW9Xg/LsrC0IE8zqrxo8pTAw3IajtcwDITV8Pd5DaYpcYXgtddea2ZXadEKPaoiRVVNGFJVFb1ej8Vige/5tFvNbPnc0y8y6Ld53xOXiQar5IbLYDD4YXjihsuTAIYJ/Q3c6T3sKiXPY2wroKoFnfYSWidUCjy/xWI6I8lK5kf7VPmC0izxAotcz5Fmn52xzZe+8BqjLENrgyAIoATPrBFC0e82Ycf2hXM4jsPq6iqtdptFluEKhySbYts2VTxHlxlFPMVQGVEnIp7N6HVb3H79JnglK4MuUjrUlk1d13hew4CMjzRVVZHnObZjoGqLwLGwhMHR0RHCC5CGgWU11cfdWUVRKCzLoSgFCEFZFJg6J/QC5jFMypp2L6CqKtJFSrvTQ+BgyQihHIp5iqEWpOWIvdmE0LUJoxZVUfKFb7zKZz53DaMCKTXyP3G4sL3KcHRErQTzJOGV114nCALu7B5QIbG8EAyLKIq4ceMGm6srBK02dquF4/kIpbGlR1VodK3wXAvpSPJi0bAl5QIrU3huG60qTM/HtAR+2GI8nWNZNuUiYffgkMCz8F2Plqyx2xF5mqEMk3o2bopJdDC1xrAF8zxlniac216hTmKyeUxpS+xWHyVtTPn2ejPe1rsVEtk/S5lMIB6T5wWqKpsSY5YilEZphVAaaoXvhFiWRxJnFMogrta5dv02d/emZCWc3VpFCMF4PCbwbFyvy2AwoN/v4/s+XtSirmtC32Nvdwe/1SYMQ/I8R9UFRZYgVEm33WY2ye9XCrOMrbPncGyPOM5QtQG2RbvdxjAMer0ee96ItbU1XnjhBRaLBVlaUFYVhhR0uiFJXuO5DvP5vFmgxawxVE2WJfTxBHBDAAAgAElEQVS6PZSCPE+ZTcfoQtBtt9g9mPPxDz1OlcxI87yhG7WiSFNMv8DxW6cdF2GwhioyZqNDXn3tNl/44leolI+hKsIwoixLwjBE9XpMpgssyzpdKGZzYw3HNplORrxw6ybnz22ztb7MaDTCsgwGa32yrKBKK16//ioCSa/dQgrQdU2nFaHrCpQizxL83KEWoKjxDInnOmxvrjNPCoaHE86cOcPzT3+D4XDIodY89bOPY9ouUivy406S5eVlXNuh5XvEeUaSpfQHS4yLivPLZ9nevog4Vga+XXtbIBaGidddR1cxxWIPs1ZUqiaJE6qqoMxyFtMZR/sHVFmB1IKilmS14M7uPkfTGXlVsbW1TV1XSJnjui7nty82A6HI6ff7LC0tUZYli7Sp7O1MR3iBT5kmLKryGMgpqixQRcbhbIztyCYUEIJ+v898kRKnOV7Y4fBwRHgMyDiOCcOQ5eUek8mQ1dUlLGuNg4MhSsHOzg5FmRH5Pp5nYAobrUvOrnZRSlFUOY7jES8yEmHhiS63797FMAyu5zkXLyyx0XdphT5KgHRtHK+NZVnNjCNt8roiy1LS+ZTpZEKcwdF4wazS2EIhporJZEJVVQyHQ+7tHgBNeTcMQ2SWELsWaTzj8atXELrJSVZWVhgMlhoRDiaf+7PPoWuF77msDpaI4xhlKLRuKnRaazzTBl1hCEGVpygvYDYZIU2L0HOZ2TbzNG20LmVFXCi++JWv0fEdfEeysnmGNCuYzWNuDG9RVRWbZ7YZrK3SWl7n7Po5ou4ylhe8YxrjtwdiFFDjLW1Tzh+h2HsNVMMjFoVCVzW2IXFNm1mVkMwK4tpgOM9JlUPUqmhrST8ySBYl/ZUeFy5cIM+b+Ko2YDabcXSQYpom3d4a8/mcRZHi2yaVBNeRdNoBd++O6bVCFrOKVruLGwYcHOwRRRGvvvoqg/VtLDcgiXNWNzaZz0bUdU2n0+HevXu0220c12F/f9Tc/OUOKysrPHJxi729PbJ51sgiW01SZ5kuWmuqupFmqnJBO4goCptu5yKvH4y4e5CSaBNtSizbZp4lhJaFZdsIw2AymSDtmkLVRKFPndsopXDcNoukAkeipabT6XD16tUmpNreZng0oSxLrl27hmEYrAw6BK7N6uWLKKWwbJd26ELVaFAODoY89+I1wqhDvhjT70ToKsd3TBy/he+7jEYjPM9DKkjyjHgRE7XbFMkcLQyOlKK3tMzW1ha3qooLFy7wwnPPY8YjVGVx53DG2sY2Ry/fIQxDrt/cJ4oiwsgm6PTw2h2UtACDusxRhUQQ8dbrdPfte25PetA0GjAQtY1RFyhVkJcxZTlDpxXUC3RVUKQlqoRRppjO57Qjn7ZvsjoYIHRNOwpYXRnQHyyRpulpnX4+GrGyvMbu/iGOG7KyOuC1G9fZPHcOp9ViOp/hBwG24zBbzLFsi7QoSSpNkmUUVYlWGse2SZKcdquFlJClC4ocVlfWuXHjJtKw0BXYpgNK4FgucTynFbUoixLbslnqhXieRbsd4DgSqSqiwKEVekSBSzsMsaQm9E10nUJR0vZMXnnhLhuDVaSsibo2pisxhKCuG+GUJQWm30UYkrLKKOIxn/7yHtd3jlBYtMOIIJQc7N/DRFAWFZPJGNM0T0U0pmmhtOCFF16i3+/T6bY4Go8ZrK3z1We+SZwqhFEz3LvF5uoq7VYEWpHEC1zPJs0Ssjyj2+uQ1wWVqvB9D4FG1WBhUCxSjEJjS5N2r4NCs3frNlktKMoKgSbyXbotj9WVPqoqMA0Y9JcQGsIgYHV1hTTNGY2GLC+v4oYtxFus0r1jIBacrKkmkL5LVWTUqqLIF1BptFYkeUmtwbJNekvLDAZ9XM9heXmJqq7o9TuEkY8QmjiN6fU62LbZxJqDAaXS9FdWGKyssLt3yMbZs5x75DIHh0M8zyWKIoqiaETcx6v5tFotHNvCtiS+6xB4DkmaM5vNCIKgUU8Zgtl8QrsTkWYxa6vLHBzusbm1znzRJIp5njMejxFCMJ81wEmSpInPHe9UilnX9X01m2HQ6/YwpaDMc0Lf5c7ODqtbm3RXVkhrA2FYmKaN6fi4YZfadAk9mzzOmSSC//MT/5ak0IStLp6pyfOE0HM5v73N+bNnqeuKl19+GdM0GxHOvT3iNGN5dY3xdEpWlpS15utPP8PwaISqFIvFhMcfu0QrjO63V2mNRuE4NmEYkqYp3W4X0zSZz+dEUQQCkjQBrRmNRswXc4JORK/b4ZUXXqAsCgLP5dyZLULfpdPpcO3aNba3t4miiH6/T7fXQ1omfhjgeCGu55FmBb3lVXjLsp93CMQNfEVzHsLE9tuUeYaocshKFKANE2lLbM/BMiR5nmKaBo5jNdxu6JMXGf1+l6zI8DwHKUVDRVU1hmWjDQMvijgYTlhe2+RoukBjEAYu0GiCoyhiMZ+d8qRRGDCdjPBdB60qpNlQRkmSMJlMaLfbxPGCwWBAEATs3rtHGDaCoDRNcRyHLMuYz+cIIbCPlV2O4zRla7OREU6nUxzHIc9zoBGCl2VB4DrYlqTIU0SpKfMFeb7gwtnzaCEwbA+Nie1GuN0exXTMdJLwiX/9Ba7tjCi0ia5yNpZaSNtiqdshcByODg9ZLBqAnX63MtjdP8B2PeZxQhi1OBpPuP76TZb6A3zHwfdtdu/dITxWjSmlsG2bOFngeS5p2hSoTtRrtm0TBAGKGlDUdXN8mWfcvnebIku4e/06iyQh8D0ODvbodFocHA5xHOeU/ux0OoStiKIqaXXaOF5IEEXEScby2gbvBIjfvi/X0OSxBlqE+N0VvLBLEEUYlocTRATtDsI0MCRYtsR2TEzLwDDAdW0Ggz5CaFqtENs2KcscITR5VSItE2lbHIyOKJVmOl9gWja245IkCVmWAU0xJYoikiTBNE1u3LiB53mMx2OiKCLPGyLe933Onj3LYjEjigKUqphMRmhqpCnodFuEkY9SCs9rvK3v+3he085kWU1lTinVFDwMgzxvElLXdY81shpDlHiO4Oz2Buv9NsuRT3Jwj+Gt16mqCmHZBO0emBbT2YK6Kjk8GPGNa3fAsGi1u01J3pJsbW3R6/WYz+d0Oh263S7j8fi0FSpOUqRpUVY1eVFxMDwiyXIuXroMhsm1a9fI85wwDE+LQ0dHR9y5cwfLspjNZhRFQbvdJoqiU71vHMcIoYmikHY7Ii8y5tMxk6MhBzs7RIFHt9PCEJpzZ7exzKapt9frYRgGrVaLzc1NZrMZ+/v7p9pky7Iahdw7ZG9/8RQBYJyG505rnXgxxMprPAzUfEw6K5CGSyWnuL6NbXvUlcYPzGNJXzPVe57HYlFj2C5Bq0NSjul3l9g/nBFGfVTfa9padIVpGhhOcFwZlDiOSV00IAVYHnSp6hzp2kzzEg3Ytt0khosFYeDgOpLh4S6qrjFqTTdsMdw7aETdEoTQVFnCZFjRa0XcOxjieR7L3T5JmeNGHj2/j+M4VKU69dphK6KMYwzRPLcGHtq1iLwzTHLQuYkoTIo6wfVNWpZkXrh88g++wFQVdKOQMPSaJK+1RGhauKbE921avYjRYY60HZJFxuH+IZPZhLNnz1Kpio3NtWZdD6U43NulrkvOntsiCAIWkzErPYHnO/SXtpnOjljqr6DU/aW7Th5hGGJZVsOoSElKijSbFv71Tp8CC5wWfbcB/b1791hbW2NjeRnXddnd3WU4HnFvdMi57TN0o4hiEeOtbKC15uzZs28beif2ji4oqFEgTDq9bWaLOWZ61Iy40iPNYmzfJ01yqqpCq6bHLUkSpJR4nke/3+fO7h6mkBwcHNDpL1HVNf3BAMP2qOX9BQpPEpv7vVpNV4Zt21RVhWU5x3x1hiEsQGKakul0wdraGlm6YD4fn77H87zGQx6XPx3HYTKZnJZz5+PRaSUqjmOiXqf5zbrRUEjTwPFcDg8Pmc3mONLADYPm/ByDrEhJ8gxXhfhho9X1o4hKGRwe7fCXT9/m5t0xbX+ZTmiddkdICVEU0W2HbK0tY1kmntcwJFmW0Wq1uPrkVUajEZPJBMdxuHX3DhcvXqTX650yNHVds7W1xdLSMtPJmDRNSZKE9fVG+beIU1qtFlJKRqMRrus2g1M3M06n0yEMQ/btPaJWh3GcIy2DulS8/PLLDAYD8jxHGIrrN15hc3OTKIq4t7+HqisORiMuXX2SeZqztbKJ9ALQxjsRTbzdmPhhE0YNwsSwQuoqQedjqAqKLEZqRZnHVFUNGOR5QVEUp2LrwWDAwcEBUbuNaTusrq2T1/Vxq7p5uj4w3G9KLMtGqNL0aoGqSjqdBlxFlh234zcL76myZj5f4NguadpQSBvrm3iuz+1bd+i2W8zn89Nu5qJoxERZlh3HxJLDw0N6vR5CCKrjVnXf9zGkJKuaBVfSPCeIQsIoIE4T3MBHSrBcmwsXH0HYJsJ0ENKirCqyvGS6yPmtf/q7aLtH6NkYhmJzc5211RW0rrl18xa9bpuqyCmLgsl4zP7BkKwoyfKc/YN9JpNJs5SsqnHtpho5m8149NGLFFlKuxVS5jlVUbKzs3saOuzvDxmNpghhcnBwRFWVDV/sedR1zWg8ptPpnEoIVF2SFxleFOEHHqOjKWEY8sQTT2CaJotkymNXLmE7JmWRsbq8RBB1uPLE+6gNi5WNbborazQNeO/MAirv8NKuzYqTdQ1Bb4VyaKOO4x+lSurcwhBmo1eQNmVZkqYp7Xab4XDYTL2WxfDwCMt2kYHH/tGQsjZpdZZOm05N0zxdiukEcO12RJVLFosFaZpSZeVp9c91XQwh8bwmqXn11Vd5/MplZrPFcW9fTZqmp17dcZxTkYzneUgpqbKajY2N06w9aDWgn8/nlFVFezBAKcVgZRmURhV5Q//ZNljgeQ5KCpI4J3hgiSzLcvnd/+vf0F46j/Q7rPbh0qOPUxQFn/vc58jznLWNbdI05ZGzWxgCDnb3sG2bs2dXmM0XzBYzLMs6FeUocf//mLz00ksMum2OjlJC1yGuU6RhMZ83Xd/3dg4RotF7ZFnGxUc36fVbzGYz6rpmeW2VqqoYjUbMZjN828T1AiaTEYbZyG7jOObWrVsIIdjcXCeO5w3V14pwTYszl55gURu0+iu4ftjkUe8AtXZi7zCIBQZQGRpkG2l5GFIjDCirFCMIKbOMukpJkwVGLdG1YpEm1FKwdf4yk2nM8kYLpQW9aImj6YI4iXEsSVErEAIpDGpdU2uNadsUVYXtuZRlk8hZloXledQ0y81qo9E7x0VGEARcfd97uHv9Ju12m8U8odddwnGNBsgYCEPjBy5FmeF6TXjSXe42UstehGEYzOeTY1pN4gUuRdaEJbpWzaAKQoRoqobB8jI1Am2arG2ugtfCFALTsvnf/tmn2EskXujyD/67f4gXtRneusYf//EfEwQRWgs8L2Kw1KyhtognmK5Lt98hDANUlXCwOyHWEiEbWnBzfYXD4ZBut8toOObgKMEzTULPxnENpBS4vT61MNiPS1xXMh4ecuHcNkllsvPyDuPxmPPnzzOdv45Sqvm/KK5HUQvKuKIqS2xbHDMaBv1+nyAI2Nvbaxgco5Gc9tc3mCzmtHtLmFQEnvOOeeATe4dXsjBQgCUUlAmqyk69q+d59+NH2bS8nLTLn+gXTv4+aW8vy5LBYMD6+jp5nuO32piuR1KUDEdNvHrSUzedTinL8jSuO8mGlVJNeRdYW1tDKYXrunS6IUWZEEYu0tSMx2OSJMF1G9ZDCHEaI3c6HdI0pdNpgJTnOVG7heO5uL4HxwyFlLIR+6Qpk8Uc03UwbAvthISDdZzOgM7aNr7f4ca9Ob/63/4vhOF7OfPY4/zfn/xXrK6vce2VF/mjP/ojdnZ2mm7iPGd1uUcYOEijptPyWV3qYQnN7RuvYaJYard58sol0BWObXJ4eEgYhrTb7ZO5kbWNJWzb4JFHzrO+vn66oOCZM1ucPbvN41cvY5qQJAsMw+D/Z+7NYyzNzvO+3znfvtzv7rduVXVVd08vM909wyFnSIk0SVmULIaUQgWxJFi2IcBGAiRxHCtIAANBEkBRnMRJoERepMhxLAOGhES2TCmStVASLZKiSJHDZYazsKf37ura6+7325eTP76qS8qUAonqIXyARgMNVBfuve893znv+zy/p9lscu/ePV6/dcQ0NHj15gGvvLHHaLogK0HoFgfHtQxza2uLk5MTABqtNs1OF8dv0B8MV0/Pz33uc0ynU05OTkij6IlW3RM9EysUCoGsCsTymHD8kCINEVWBKDPUqbU7iWLKvCBaxjiui+U6CE0yX0RIzcBrBCRJStBsUlSQJBl5UWJ6TZSQSN2gQmGbBsfHx7iuy3Q6QVBLDIuiQD8trLO+ripLlKr9XHEco1GhVL1rhuESz611CGetNdu2V5NDAMuqR8KuW/MnCglokkqAaVp0O32KoqiPOLpGrkq8ho/b8JGaREdgSIEu4PHuhP/6x38SLdik0WrzP/69n0RISRwtUWXCm6+9vrpgtdttFtMp25sDHAN6nSbNZpOrVy7x9NNX8H23tokphZCCPM/JslqnnZ1avmzHxHct+t0Wly5dwrIsms0mAP21NeJ4iWkKzm0OWSwims1WzbGwLOZZRVZVRFnGIo7ptHyyvCCKExpBkyxJanuT49BsNsmVhu14ZHlJmhckScRoMuPipctYtktvbYjfbNdn4ie0nmgRc1bEoiKbHFIsD8nz04KpMpaLBVJBnqa1OL6qSLMcaeqn06GaPxGn9aVKMwzCOKEsFXmhaLT75HmBYVpMJhNaQd331HUd0zLwHIfDw0Ns22Y8Gq+eWlITeG7dl6yHISWmpuH5DqKq6suQLhEo1odraEKwjJZomr4anrTbrTqaLArpdLuUp1+Y8WRClqUkSYrlOPiNBo7v4QcNKiGxHLfuIxuCwDWZnhzy0ssPyY0m7Y0t/sbf/A9pDjYp8oS9xw9445VXcEyLnZ0dLly4gOM4bPd7fPs738Hk+JBsGVEhabdaVFXBxtoaV59+ho3NTd68c4f5IqwLpALDNOh223Q6ARfOn6PXaXPt2nWanS6u7+MHAUVZ0mo16XXbFHmGbbkUZbV6gkVFxs7eDlme0+p1yJKE+SJEM0waQYskDGk2W6RpxuHhEdN5yGBtjV6/j2mZZHmGQrKMIrbPX0SaFp7fqKW8T2g90TOxUKAJAA3T77E8PbynRQ4STE1jtlggqgpDSvSmT5qXREmCk1WE8ZJSE+i2R6kU8yik2eoTJqBXgtFkysbGBkdHR/QHQ6LFAk0ILENjPJ7gnU6JsiwjSTJM08f17FrTkdaxAnGcgchJkpyGZ+PYJuQG8/EY3/fZf/SIbre2Ebmuw2Ixw3Xr4UdeFvjtJos0xtINTo6O2RyuM5/PMW0Dw9HJJdiuR1VUlBRYjR7emo9Hweuf/zQNv81Lr7xOojX4jve9DcvvU2U54WxGESa4msYb9+6z/3iXhuuxXC753ve/n3/0Mz9LFEWoqiJoB3z4gx+kyCK0Tn0mbHQCPvR9H+Y3P/Y7jE7mvPjC89z+6msMewHntoasr68TBAFOI0A/zVMpigLTsjF0jTScEy9CsiImjCOWyyXNZpN+w6X//NuI04Kbt++gqqLOTEkrFqMFpqNx/9EOw+GQVtdF1yzyNCPJM7I8ZxnWm4xjmhwf7LPV7JBlWa1TeULrrcF3qxKlYqT2NYLk2eOtKGqGUBzHLJdLTLOe2wN4nkcc127kVquFrusopVattHpUHLK7u7uaWMVxvKIHnd3Oy7Kk3W7Tbrcpy3LVxThz7BZFgeOYOI5FliUIAd1uE9OU6DpIWVGUCZqusGyNdqeeBB4dHa1GqVEU4fs+YRiufvd4PAZY9WxbrXr3FlnMq1/6A7JoSVmWHI9HdDodXnjhBTqdzkoDUVUVx8fHSFkbA9544w02Njb42//df8+b9x4xTjIOqfjq7Qc83j/ml3/lNzg6XpDHKbJSnFvf4Id/8Af46z/yA4hsyrWnNji31mY46GPqGroUqzPqWXsw6LTRbQvdtnjq8iUc110lSt29exeyJS1L0PEMvvPPvZOtra3Ve5ymKbPZbHU0qUfudUrV4eHh6t6zcvic3l3iOH6i5faEjxNnOoqcPDwgme5TFSlClUgKsihmPp+jygrbtMiKgpPRmE6vR1nVXZfqlDGUZjmabjCZzNk4d4GDwyPCJCXPczY2NmqBjxT4vksYLmme9nm73S5RFNFtd1kuF1RVgaYJomWErmvkeYbf8LANjcPDXVqtBpPREVIoyqrA8926V6qJUy1FymQyBqXR6XYxnZoYVOY1AUfX6+GDpkuUkCB1TMumLErSLMdvtpkd7LA43qUdBIznEbuTinMXrvCh7/sIfqtTv22q4GB3h3u338Qyat1GHMdcvnyZdzx7g2caPX70r/411lttbu8d0u32efhgh4ePdtg+NwAEzaCFZdkYrsP2hW38Rt3i82wTVRWURYbj1334s2GR1OszvKIkSWJUqfA8n/X19fpc7LgkeYU0HU5mi/q1FwUN1+PRw0f0Bp360u3Wx6aqoobI+LV/bjadrTaOZqtN0O3jNQIMy3lioO23JoxR5UxHB9iGQRFLDEMjmiWYhoZtGqhCIQ0dSzhYRVk//rMKr+FiGSZZkmI4GhQFvuey8/A+nU6fuFBIzcQy7TrQJk2whEGSRFSlsZrNL5dLAq/e3U3TpKoKOt0uRZkROAFpFpEkC4bDPvPxCE1WGEat7BoMesznSzAlWRLhN1w0XRCHOX7QYDqf196zSpw2FOudN2g16HT7FEqjqBTNVn3BTOKIg92HZHGI1mpTlhkbGxsMBgNM26rbj3GC6zi0212GwyG3b95G13XCMOTFF1+kJytee/AxvvQvfom96QlSwcl0CZbD4dGIL3/+Za5du8Z8vmT7yhWEaWNbNk10Gs0YrVhycnSM5droskJKAUJiWg6CAi2XlIXFbFxi2BYOgnbQJEkSbt/fIYxTygq8ZpuyyGg3mxyfjOj2B/jNFqZpMp/P6/76dEqn36s7UZpGq9VCCWi1Wliut3qylmW54kH/WdcTPU5UqkCRk4czGkJSphmG1Alnc0wFlBG2JRCyJM0yhAF+4DKZjnAsA03KetqUF1iaThLV1PI8iwgXY9JkgSEs0jClKko0W2c8PqHMUqT4WnZev98nipakaUyeFTi2T1LmmI6JokCoHNu1UJTossIsSxAlnufy6NFjihzSRUi0DJnP5yRprcGoBDXiVdNpNFv0Bms0gjaWXXczzqB6rWYb2/EwTZ1otEeRxqxvbFMoHUvT6AyGXLx6A6lboBS2baGKOiCyqMSqHdlsNnnzzTf5tY/+KvP5klLTcBoBL64PkXHO0fEYzTR4+fX73H39HjKJyZYjOg2HLF6i8ro7YfktWp0mi9kJ89E+VTIDUZILAUVBlWcIJWup7OYmzW6H0XTCeDxGYEAJvu1QLBdsdnpkYVgbSDWdk1nI0fEJeZ4ThQvcZoOjk2MmJyPGxydIrQ6OL4SO6XkrJvST5BS/Bd2JClHGlIsTqjwiiZak8ZwiicjT+sZvmTZVCaLK0IVAKoFQZU2jiTNAUuQlzU6H2SKkrBRxnOAGPkmcYzsWu3sPWB+uIZTCNDRA4Tea9bSuKDB1nSRJsKz6AmEbOlWSUOUZrqEzPTnB0jSKIsP2HVzHIE4iyrKOWOh2u2RFgW7Vww6pWSuCphAC23FXCCZNq13FUjcolSDJUnYePiCeT5FVTpYndAYDNNNEN23OXX83reEWvfWNOveuBqlhmBpCg2g2X6nOxuMxcVHwH/yVv8av/NKv8mBvn8XeIS9sbDHfO8DwGuyFU3ZPjgnHIdUyw7B0+r0epm2RVVV9XBE1KzqcjSiLnLp+MwxNX90ZaleJjaoqLMPEdz1miwXzxZTJZIRlG9iGQavVplACx3XZ398lTxPazVrDXaga02tZFt1uFwS0O12iJEPqOlle0u0P0E37iR0n3pKL3dmQ4Iw0fva3YRiri4Xv+xhSofKUPF5SJBGmpqMLicoLdATT6fQPaVuLIqHRcHn8+CFrawOOj49rn1uW1TtmkqwGKUlST+fOGLhpktR5e3nB6OAI37RZLhaYpsna5jqL5ZQsj3FcgyyPOT4+PrVZ1YV75oyez+er1zidTleX0rNdOEmSWiVnm/Q6LfI4pNFuoXRJriqUJgk6bTa2t0DUOYBJlrJIIoSh0x3WJsu1tTXe/e53U1UV7//+7+PnPvovOZ7PWWQZsyqFxYhLvk+4c0I6i8g1i5du3uPWw0Pe+OLL3L9zl6IqcTwXYdgYjofjNvAsk+nxLrPjffQqQ1HHEOi6vlIAnn1eJycn6Lrg3Ll1Gg0Xy9LrAYpSWJbFaDRCytMvfJatzKtnX4qzodH9+/cJgtrkm2UZ0+n0idbbEy1iVWkITHTdRbMMlKjIKTFMh0qaFLpBpgTLOCIv4tWjuSpLjg9PSIuUtMjRTbP+GaWhneaszZcRRZJjGzDoBkxPjk9hHSFe0GR9Y2v1GJ7P55iGj+c1KUvFMlysikzXdSzXo6hS3KaD6ZkcPX5EFRa07SZVlNIwTJaLOTrgIBFxiihrqHYYxTRaHdIkZ219SFJltNf66LZLWSgankPT9RmsnauPN7IEUWuMHbNEGgZ+q4/nNwGJBCzTqUfflkPDbWA4GkKrePToHpoome0fERw95rwjKZHotoUqcja7HdY7DUxhcLQ3we90+eQXX+LVOzscPTpiOZnVIHTTxTB9NK+F5zVZ6wzY2ugjVEQazqhUhhIVcVmiSnAtF7/RZPviU7Sbbcq85MqlK1y5dIXOYIDluyTRHEtXeIbBZDSm0+7juAFFXIuMdMvEcGzGs1prksQL4nnNJ3EdpzZTPKH1ZI8TChBQFDFZNKHKa4+drApUmZOkIYZpYpsW8+mUKk8p8pI4TvC9AIdXj38AACAASURBVKcZsIhSXL+JbtnMkgTH9SkqQZoXNByX3cc7SAGea6NUtRIDjU7bW1VVEccxujSoSlULVST4ro0mBGWekWUxVDnosg7EqUryMCWJYrI05XD/ANN1WC7mp73iOY7vEccpftBEajqmIUnLDGGYNbgFeRo4EyGFAKGRpTVIUZgehiaRAuxgk8b6dUwnqPnG1GlaZVkilSJNYvI0RJyevy9un+eNm2/iPd6hLx2k6dNoNtn2AyzTIswroqIiU4JRMidoezy484Bet8nW9iZOw6HKSkzLAAFVlSM0wWg0pmE5oGkIIdFNE8uyqYoKKrUi4DdcF01KfM9lNp1QiTrscXNzA89zsTQd0zBotVr1UUzXsV2H4jQFwPNrvbGqKoJmE99voesmXtB6IjJMeNJSTAGIusWSxTO0IkOUOapIyNMFQipUVSEVGJrOYjqmKhVpmuG6PlGeY9oepuUSRjFus0Wa5hSlohEEJFGdvFSr3yJGo5MaNt1urzQNUGuBhZLs7u5imBp+w0OTJcvZFFWltFtNVJXjBT5SgsozqrRY9X49z6PRaQAVaRaf5lQYtFpNyqIEFFmeYDkuCAPPC4jDRZ13AbiuQ6VK0jhGlNDuDRGioqg0zMY2g6svIr5+YiWgLAqODvaJlgv2du4zn82YjMbkacrTz94g3tnHSivikxMS02Q5OqLRaFIoSaEqzKBBJgt63QBb6OyPD1hfH+DbDkG7iW3raDpMwgmFUhjSYHw0IstSHNsiS1IC36cscpI0qlV3VYFjmXWYDRW2bSK02gp2hv+yDJPr168zn89X/fyt89tEae0OT7MM0zTrkXRRIqRJf22IZTnfmIP9Ta4nfiYWqgYO+p0hUrNBGSRJjGnV0sCzs2Qcx7X+9RSpFJ2KQs7O0LZt/6EhRS10r/PVHp9yHYIgYH19nfF4zHK5ZG1trW7pnPJzzwQ7UJ9hLVvDNI16iGFZq27GYrEgTVOUqoVAtZa2wHFsNE1imgaGVnMYsngBRYpuQFkWeF5AkataengaWpNlGcvltLb2+C2qUmFbPobdxGj0+KNs6pqm0e126+SlosD3fba2tmi329y6eZsXP/RhZp6O0ZK4nSbD65dJXZ3K0Ai6ARuDPi0pcbOCZiOg2e+ytrGOVBVJsiSM5hRFhlZouIbPcPM8rc1zSAV7d++xPBmRLubMZxMsyyCOQ4oio6zylXWr1+/QarVYLBa02+2VJvnMn2dZ1soSdrYh+L6PptUS2bP7SiMInlgBw5PuE4s69kkiqASUpkaug9B1yqXC0nQm02Ns3SAOI9p+QIlgOlvSaPoslY3huIRpim2YuJZLVsREUYLjuCR5iaFVPHX+XD0F1CrCaEGv30HTNObz+cq7FcYRWZ6wvtYjTeb0+g3GxyGdTpPJ6Jh202ZyckyaJMii5ODoiHPnzjEej3n06BHrW0Nsz0NpJVlZ4OgmumZyOB9TpIr1y0+RlRLbCrAdh9lsnzQvapWeZdPxfExVUEobrRJUFSjdwjT9b3jbsrIgiZaUWQpSp722xvRkRKvlM2h3CbPf4/L7n6d9ocsf/O4neOe73sPP/qOf4fs++CE+/rHf5R0vPM+b9++TlR1u3LjO+oXzbFzZBr1+ktiWQR7HLKMFA89BWTopKYHr4OYeoYAwmjKfaDy697DOGTy9mAdOk8VoTCNoMpkvKISFZVmrjUU6grsP7iOEYHNzE2loKCFZ3zxPWSqqqqDIKzRp4Lo+l56+Ugc4yn9Lz8S1/EfUiqoqJYsnUMTIIkcWMXESUpUllmGQhhFJFBEnKabtoaSGHXTIS5CGhdA05nGKZXmYZu0m1g2Tsqq1rGWRY7v2SswdhiGmUVNsyqIgCkPKLMUQBZQZkhxNKIo0wrZ0ZJljaTrxfEGRZkipr+SUnU6Ho8MDeoMBeVGg6TpxkpFmOWg6umEiTUnQalFWgiiOUFWJEDVN0zBqN3SVJ1SijkkwbBcj6NPonUf323z9gVBIiURRpQkHjx7RbtjoSpEsl7QbDR7v3uXRwwcgBUezKZNozlNPX6HQJcMLmxxMT7jw9FNce/sNgrUO5y5u0275UGToVcnieB9XF0wODrn55ptYrsdsPuOVL32J26/f5M7d23iNBo7rMDo6YTaZcnRwgC41wsUS0zBod3tIXSfJ6yHFWZfGdhzyIsdvNNANHce2WcYJnt8kzQtsy8IwTGzbQdMN2v0+puM9URXbE57Y1TsxSoIWYFk9Mm2J0C0SitWUJkszfN9HuS6zMGISRnS6A5bLJUK3cR2vlluq+vig6ybj8ZiN85cJTw6Jo4jhoEOeJ6eukQqJQBNaLZJRisnJLu3Aq61BsoSyYDGZMOz30ERJEWXEUYQoKgLXq4Urp7yzR48e0eu36x15c4NKQJSmeK6Jq1uYloMSBXmeUChottoIDBaLBbquoZ32XoWmoVsWum1T4GG459CDzje8a2UFlhRk0YKf/LH/iheuXaa3NuDtL7yD8ckOz1+8ymy54M6t28yXC3aOD/A8j+/4wHcym8349qsX6/wUQ6cStaO8zEKO799j9/49ts4NeXR4zB98/suczEJefu0euizZurRJ/+I2vW6Xq5cu8/jxYyzT52D/Yd2JWaYYrkmz2cDwHNoNH80JWS6XOG6N4UriOt7r8PCwdlNnKY1Wl6qq6HQ6xOFyFSV8ptd40qL4J25PAupaFgam00LqLoXUKE4T7j3PI64UptAoigqilGarSxTniFNzZ1EU5GmG310nXKaEYchwOOR4MmG4NuRwNyMvFYau14oo02Q2mdIPumRhTBiGlFmM77exdIWmSizdwjJ1yjwGSkYnJzUHI45xtLoAoT6bbmxsYDsGJ9NJ/cg0dEzbQncs4qxC1wS22aTIDYJ2HykMijzBsRurkJY4XlIlMe2gR64JbLeLsFvo9jceJwwJr33pK/yDH/9v6XkmZp4zebTDL926Wcs6NZdpuOBv/Od/i1/85V+CSc77/8J7ieMYw6kzMJQUOI3a/S0riyic4wUe25cu8nhnn4PjOfcO5uQKqjLju977IueeOYfh+pi6xe27D8mimGiZsFjUG0G3OyAtcizHRugaStValcViRrNZm0+T5GuZd1evXkWTgtkyXvXYpZSrqK/hcFh3YZ5s0T1hKSbGH/pflTtAs46whEakBwgLknSMtAvCRcrsaEGuFH7Lx/INcHs8PjhkY/sChtAolInf8upbbprS9gOyKMazXDQlKZIackJRYWgmaV7Qbrk8vPUFNrY3sUwNy7SQSmc+C3FsH8cxSaMJgS3Y29sDpTOuKqpE4fk+Ozv7DM9tskxmDDaGxGlKw7Mw9ArDMtAtE8vxyQHTME/DbjTKKkGXFigNUSl0U5KaPQqrCUIidA/ba6NO36Ov34sWOw/4b/7Wf8l6O+DtL7zAxsUtvG6HL3z692md5l1vVBUf/YWfZ+/xY8bTYw4fXSHLslMSkI2j63SaPo5jgVYXThzHfPXmbR4fLFBKsd4OaHdcLl95iuHWEKXDcjTiaG/C490xWRkShXPUKdlSGhpBawDCJMtLMDQCz2EwGBB0h+wfHWEnkjBOGQw3iNMcoVsYdo2zpchwbB3LtfBabexWG2EHlJXgSeaVvzVSzNNVVRC0BxTSxbY8TNNGKUlVStI0pxQCqRvkRcXJeIJu2ayf2+Lg8JhlnKxC/jRNo91uo+kSIRSWpSOEWsFM6s5GxdHRAcvlkvXti3T6Q5qdHofHY9K87kZMJhMODg5OJ1H11HA1QQw8LN/GabjEaYTnB+SlwvYbZJXCdhtI3ajDKHUdy2niN5uYjk1WVJSFoiyrGvqSxWiWjee3EJqOMF2E5WB5Hqr6xjTke7e/QrPlkqocbzjErGyqKOXGc9dZe/oKzzz3PL/5W7/L5as3+PRnXuLPf+cHef2NO7z2+m3mixS/2WOe5CzjjIc7eysxTh3Ck/H0tW0+8N3v5t/58Hfw3LWnsGSByBIOH+ywf3DC3Qd73L13v0bgbm3VWFbbxvM82u32Su9wJo01T93UZ9LY+XzObDZbIRQsy0JKSbvdxWu2WCYpUjPQjFoC8KRomGfrT50o+qdaCqgyRvdeQsxusTzYIY6PScIpeajQDBeFJMoKilKRmy0arTbCqAsjjmuuwpkGWSExNcjjJaoq8F2H8Xi8yqKbTSbYroXjOzQCj8VkUkeAxUuqLEUnx9Qq2oHFw6++wXIZ0esOiaKkLkzPJaeirCocy61F8K0mQpNkQuC6HQyngeMG2P6AsqwhLkWZQVFRVjlVVZLnOY2gid3oUhoewmlheUOc1rkVbAZYMTQ+9tM/zi/8i19nElUcTA75Kx/5IfL8mP56h4d7Y9Z6fQa9AR/96Ef5yEc+wic//tvcuHFjRbI8GE2IowXDbgvH0Hj2mfMrXa9m6DT7XTqdDmEYcu/2LcpCoRsuO/tHvH5vB1XpbA6GbAw8hut9bNv9WlC7W3MyKikohMLVdZI0J+gOqYRg994O+/v7aJpWE3/OP3V6N9ARuoYwdCzX59z2U+i2S9Bsr/QnT2q9NVLMs6UAYeK2hkSze3DKmY+jjHAWY7kSx/MxLQff9pmVOqbts0xqS8vZZaAoitrAmcTook6mtB2H8ajGs3qeR5bENaWy3ycDikrQ7HZZTEZEUYKr1b/+6OiI+aRifX2dg4OjlSZiWWQITeA6LlGSkBcw2NwiLQs0QydoBizDArfRJoozirik3QmoVEoVZRiahdRACA3D0LCdBpbnE5UGmtPA8lvUxVtxdgE+M85Ob73Ke68/wzg1eHNvj1/+zKe50jfotV1OHo84OBgThl9i+9JVfuU3fovNQZcwzZkuI9JSsXN0Qsv3OBjNWe81GY1Gqzji0XhKXIAmbRaLJUmls38y4ZWvfKnmg2gGnuOS5Yr5dMpav7NSmSmlmM1mTGZTnIZPo9M6xe7WWhLDtlckn/39fQaDAY8fP0bXdXq9HtLQkZZDo9nG9Xz8Zgt1+rqfZBE/YRXbv7kKSikRlsniZJdiuQNSkiuJMg0MdLJSYXselRJgNxDomLqByqsampImNGyTdDnHsATxYo4qSvIkQZZ1ev0iiskrSX/zMhVaLfwpijqYvKpoBgGOaaCbBpbnYnoNEpEjqoIknKMsH10a9UVTaOiaQXNtCFIipYZt2WRFSVUIdN3Btj00w6QsSnRpYlkOuqPQEKgkxzNddMcnrQx0v48yBlhu+/SDO/vzNQjMKApJVMx8eUSlKuzAx7Y90iTlwjDg5PiQ9fUN4qLi7oPHXNgcoEl45vJTGJrgPd/2TjaGPXIk1zqS1vnrRGHBo7t79LprNDsBR4dHpEnK7kHMZJpSFop2s0m/0yGJFkTRlPXNTTSpn47Oa+hMUqUswwV5kuNoNrrfJVkkNCwdpZXkRUlWFJSVJMsrdEun3WljmAZSl7iex2AwwHV9hKajaU92F4a3eic++yWnMaupqttvmjTQZMEiyXD8Blkh6g6A5SCFgaZZQIEqU7KoJlMmUYitu3VEbpxQFiVKSAzbxtEreoMNpNQJgiZJWqOmPLd+dJmGRhovmU5GNAKnBppUFnGe02g0KLQ6pqzZ7SB1Db8ZMDu17yulKMsSLAfDttFME8OyMWx3FVauVAmlQkgN03XRbZcCA6E7SMvDb3f4o4QCZ9PE3vomTc+m4TaQtx9yqd3kpS++zPFxxl3dxnSaJKMZnqXz/NXz3Hj+HXzuc5/j9sMvIqXkE3/wEu975zt48d3fgTO/zzyN8FoeZtNmHC04fJzx4MEDNE3j8e4BluUwHA6Yz+dMp1OEECs0lmubpIuUKKnjIqRlU6mSsog4PjmkazqILCEKJYbh4jgdWi0oC4FtOyRFhtQMpGbgNny6vTV000Y/TV16S+rrLflf/40lqD9sQ3epyhRVJZSFRHod2hvnWCxjUgW+XQNHqkqCqSGSOlwwXtaoJNO18S2HUZpRlJAjafst+q0eUmrIStURU1p9XJjPRkwnE+aqxFJ1qk8jcFgsplRlHVWWZAmZ0OroMEMnLQtSVa54bys9ht3AsDwsp4FmfS0Z6sw5UiQlmm1iWhaaYaNpXXACtGD9j32bz3akizfexZc+8RtYns9g0OP61S1cTfCvP/0FlmlGCjQ9l95wg/3dh/zY//S/cONt7+RgGuEFbZ6/fJ2joyPufPLzvOuZDU72dpjHIYtwycMHO7i2u/K4Oa6NaWpUKsUwAU3HNF2i5YwkSRhNl0RJyjNr5xiNRvSdNb788kv0BwFsVJwzBYvJkkUV0/KgNJv1uD3oMp8vaDYCsizDsm2eunIFzXSQhglSP9OHPfH1LSniLM9IkuR0DFlnopmmjTQDKjTag3WU0MmFBkpSVYIsqXdCW3fwHRNdCnJZroTumqbRC5rYfgNpWlQllHmNeT3rM1uWxYULFxgd7iOzOjJhNBrh+w7LpKijwIqKaSzQbBNpGlRxzmw+J08V0WnOtGEYZGVFw/MxHBepOzScerxdliWGtDAcSVIVSMtEGA5SemA1EJr9x354Z45jzW5w+dqzqOkaT11YMj1+gCwi3vf2K2RpgdYe8Puf/xKl6fGJL76J6TTZO55QGD4P7u1ycOdl/uIHvp3f+N1PIct3c/uLX8ANGoyXc7q9FlvDDoPBoA6+nE2Zz+cYhkYYZqRZbR4NgoBut0VaKIYbPdK8IM0LXv7y67zyyuu869uf5e3veJayyDg5OsRxddyOjW4VdZaJYRGGBwTNDucvbgEgdRNpmAipn6qWn0S4wTeut7SIFRqyAq0SqCIHw0GTJrIU6MJASh/DalAqHdDQ82g1RtaLFNNpInUdofu1NyspSLMSVUgUGpoXUCDQVk13gW5q5EmJ0iSVUhwdHWFISaPd5uRgjyQO0SowG320ZJ84HGMGHoWCaDpFU9BqNljEMablInKJY/tovoNuBBhmC6FDXCo0lSFVRqmgMHw0LUDoTSrTpfTaWEbAH1fBZ2IoTdPQpcbG5ef4zV/8eda6PjvHYX2GZEl/6zz989tcvX6Nf/qzP0fH1pgsSnSz5OBwh6uXXuAj/95/yqOXfptLLYdwmdPve2xvr9PtPVMTgloOlukyGS+YCAPb7/DKq69imiaB0yBTCULp3Hv4gF5vyP7NN2vVWZ4zSuYQOJS6weO7d7B0nXm8xPIHnOzP2JAnYDlUlo7uOXUeh4LecBMh5eqlvzUHiXq9xX3i+swXnqrEhBCkae1Y1jQNz9VJ4wV5ukRVGWEYrmgyZ/irM2cH1HYaxzXRDeh22zXwpMxrjYBGnWqpchxTR5QZlAWeZeG7NtPJGM/z8H2/RssmGXbDI8pTRKWwTIFjm+RpxsneiPloUhMxNQmGhq7Z2LZLpQryPEZWteoNWe80libRrYDKX0dvbdcF/Md8dGe2pjPrvGEIUBXv+87vpt0/x/b29gpROxqN2Ln3iG4z4K/+8L/P+c01hKnT6W7y9LW38d7vfB//+P/6pzzePeDbrl3ke168xAvPXGDga7ik9FoOShpUUkNpGnGUcPPmTSzLIggCTk5OVtZ63/fZ2dlBqboHn2UZ+3vHjEcz8kxRFBXjUcj+3pj5NGN/d8L+/j7z+XxFTjr7rM5kqd+K9ZYW8VlTu45SrVsrZ9xb0zShjDC0AlVEjI8fr2jljuOsUP6apq0kk1kes1hMsB0dXVMUSYwhoEwTNFVhagpZVciqxBCgiwpZ5YTz2uZ0lnZpGAZlnFKUJU6zQTSdU+UhppSUSUGyyKiSjOVkRpSlVLrEc1tomlFT4LUSQygMXaMSOtgNlNXG9HsYbpuitIA6Kejrd+GvjwsWQvzhW7pm4A/W6Z67xMc//nE6nQ7r6+sAjA6OmY/HDHsdfviH/l3Or/ncee0r9H2Hf/7Pfop8tk8raPDC89eZ7N2n4Tq0Ap/z587RbATkSnL7/kP2jkaUqFUcge/7nDt3juVyyeZmDb/u9/s8++yzzOdzHj58SJbl5Jni3t2HbKxv0em0SNOYvf3HDNZ6HB8fE4bh6r09szjVF963srq+tt7S40RVVQgkk8lktfuegTeKoqDIYqRhUihJFickmb5C7b/88st0BsMVgDCO41qIrtXxrFKKGqFa5hi6JAqXuGZAEoeIPCZKIxqeg1AVjmlQIjBsi+VyCUrhWw5hdoLluYhKA0qEKjENg4OHe7QDC8PXcH2PVq+LqupwdWkJlMhQ1Vl3xMUIBiizjzA9UBW6ECsZyR91lPiGiZU6hW4oidvsYhgGr7zyCttbm7XkMSt49OA+57YG9PsN/tL3/nl+/WMv8eoffIrtjYBnti/x3d/1Pdx5/VXe884Xeby3w2w+Zh7noElG4wmm5XDr1k38Vg/HcbCsWvC0vb1NktQRER/4wAfwvCa+16Df71OWJV964y5KgeN4pGlOcvKYD3/vd3Hz5i0ODh/i+Y3VJiOEoN/rY9h19ontfEuuXG9tEUsUyIpe1+f4oGJSRMyWIce7E/YeHZNrJXml8Bot9vaPef3eAUEQ1AWbZewe/svV47+qKnytYv18n2euXSJoeWiVZDGf0m02KJIxx7sHhMsJgdlmPp3gWDWLQqEjS4PpYonjWeRaziycocqKSiniIsYuhkhborsmwvOZThdsrgmanouhHOJ4hGeWaNQXu7gsafkD6F6mNAO0M93I/9/78ccJwc/+XYAm4Qd+5Ef5J//z32at16axdoG1fsHR+ISkLMkTgetY/M3/5Ic5mS44PhmTRSW2prh4dYMvvPoS1y5d4ehwj6pQ7O48JhcmDx8+YLi2RlwpOp0WySLkxbc9z3MvvIs79+7WLOd5TqoifvFf/Ro/+IM/yPdubnDjncd88fOfQxYJJQYnh0eYmsn73/Ui/+pX/1/e98N/nXlaoGkm8SLFHzgYuoV7eqz4Vqy39qsiNbJowWR/n9EMfv1XXiMtK5552zt4+/d+kL1HD9g9OOR3Pv1ZpGGyEC6Hh/PTmALBZHdOWU5Ws3hbWCyLGWXyJs9dv4QT2LimTrSYIKsSyzJRmYYuStZ6LVSR4TebdTys7mI7OmWZYlse4XJBWWkUVYXbaNdN+6xAKcXx8TEt0wJpgG6wjGKsQRvdsPGkQzqJyckZZQu66wE5xhO9uGy87Tovfs+H8bIFjx89xtzosbm5Savb4eGjR3z+c1/lL//I80RFxobfo2UOWIZzHj7YhQpmYcxotmDv6IRer04OXVtbYzabUUQ573zPezicjLhw42kMUzAfH3Pnzh12d3f57g99iAvnthBlhY6gLBKOjvc5OTnBdB2Oj3f4yutv1FENwuThvftcfe7tmLaNadqrcJ9v5fqmtRPjcZ1hcfbjX3++qzXAdVtFqzL+wd/5MR7c38HQda4+/TReUFtaDg8PuXXvPkfHI+ZRwiysW2RnF8KzndR168GCrik6RkXflTz39BYbQ4tWw0GjosprNzNlRMPpEGcphl3T0/M8p9XusojqhKUkSZBVTpmnRIsZjqVhmxZRPEMKi0994su4hsv7PvhegvVNpNOmFQTcuf2Af/3bn2B3dx8tVHiOT2Ja/N1/9vPkfn1+PWMu/1lWDhgq4yuf/E1uvvRpZouIzfNbNFpNbMfhjS+/ye999jP8Z//Fj6JExd6tWxwfjzCNWhA1m4+4f//+ihUnhLZKTb1y9Rpra2tcv3EDw7b46D//fzBNky9/+cv0+332D475oR/6S7z00kt8//d/Py995WWiJOXyM9cYbm6j0pjJ+ARRZviezZc/8Xv85f/oP2YpDQrTotPZoNlsPjG6z59kfdNj5zNQ3Hg8PlU26YBYWYSEqF0eP/F3/w5He3uU0uHGc1cwLJ2Ht99k7/4d1rfWuH/vDvPlHE1CtFySRgvKLEZUNd1SAOFySVkUiDJCaFBWigrF1Qt9hr02oipAKaRQCCrKQpClKRJFniZkSYwSFUqVqLIiCiMM00TTTYo8RzdMhCrRdY1wGSGFzXQ84pnnbmB6LW7d3+Nn/+H/yZs3b/P48AR0ndxvkqiMjBl37rzOn/vgX6QoBbqUpzatb76trykYH4959StfZHu7x91bt2k0ApaLBQcHxwyHXfxmm3/8T36OZnONaH6A53uMRzOm0xk3b3+V/qDPfLGg1W5z5/Ztrl+/xvnz28yLHK/h49k2X/z9z2LogjgMsR0H13GQUuPhox0cxyGOY7a2N3n+He/g/IXLLMIYQ9cYrm8yHY+4f/s2P/iR7+P1u/dob24hTZt2u7fii3yr1p++iBVQVcjTy4nruKg8QzchL8GyHGSVASU/+RP/K7//mc+wt3/EdDpBhQmjoxGe2yDJSl5/9Q3CZYImbah0wjRa5cKVZUmSl9RsHFFntBUlyzhjHsbouksZV2ye72GatQG0yMM6ud6wiWZLHMMkCSN0WXcSDE2SJxGGVCRVDd12XI8kTushiypASHTdZb6YsP3Us/zv/8fP88nffxWhNKRm0/CadJpdkqggjVJszaEKU97/we+m8jroFZSyPCVKfHOrFKCpAlmliKxg0Gty985dLmxfIUsKJtMjer0Ba8MNPvrRX2Y0PiFLi3o8n4RsbgxZzOe0mk0EsLm5QbMZ4LoOb3/uBQLP57WvfInAN7l76yaiUhhCEscRaxsDrr/tBm975wucv3yV2WyGbpjcvHWb8+fPk4ZTfu03PoaN5Mb5c9y/9TrWYMBg+zKd1hrIrwm3vlXrT13E8XKOYZlwWl4o0E0DRMViNMI2JEpVfPy3PsZP/dRPc7B/wPbGOVzTIo1CXNddOZ37/R4PH+3UqKpSIc2v4ZQAiuprNJqyLCkQUJUURc54MieMFOPRiGvXLqJpOQY6J/uHfPJ3fpuL5y+ys/OIVqtJFC1reJ8Q+L5fxysM1kApJuMxZV5Q5eUpgrZgOc95OIf/4Wd+gfsnKUF7gGUa6LaL7QfsH4/xHJeyyGm3mpiawO116Jy7iqkZKAnyz7AT52WF4XMLNgAAIABJREFUoWt4jkOpKpbLBU9feYZP/O4nufTURYZrPaaTKZ7n8trrr9Js9CiSirXBBqPRlLSIaTSbtNoddnZ3efrqFWzb5tGjRwyH65SqYG24zmA4xHc9lsspnmPw3ne9g9ffeIPNc1vcvHmLTq+DZmoMNtZQmmRnb4+W73L+4iU++6lPQRZzuLdDu9/mqWduoNktDLPehf8tLuIKwxCMTo7I0hjbcU4Nf4oiiznefUgZh1iWw2/+9sd5eO8+ly8+hawULz7/drI05ujoiLW1NaIo4vDwgKIssR2PslJkZR0/VYM4SpA1T+0sIDBVNf9WKcVsGZKUFbrmcGFrE8PQyFTdn10frHN8eMDly5eYTidsbAxBnoWk1GbSMM2wLQsUxGGEqTtkeUqWlqQxvLG/4N5U0Olv4VChGQaW6zOZLzFtD88ycCwLgapDIFsBz73nAwilUcha0fbNLl0KpBSYpkWpZJ21vAwJHIfJ8RFFnjMYDCiLlLX1Lt1ujzyNiaI5aRqTliXnts6zCCOevX4DVRWrxNWNzQFJGpMrGGxuc+OFd7I23KA/6HHr1ld5+upVXnvtNa5du8ZnP/sZrmxvES4WUFZsbWziug5+0OILn/0sV86fIw7nZNmct7/r3RhBH6nJb2kBw5+6iBWI+sJl6jpSr8fFCEWlKixV76D/9y/8An//H/40vucjlKLdbJElKSgIw4jFMmQynSH1Ot8hTBKQGkqoU8p7rVwrKrUK/zZNkyjLoSpwXBfHdZgnEVqlYwmNS5cu4TR7VAqyNKbXCaAqMS0NTRNIQ8O2a+GOEhJhGjXpRkqODg7Jc0UaRxwcHLF/MGZeGeyMY1RR0XJMDNPEcTzanS5S0zF0RVHU1B6dirXtc1x/918AJSmleALdCkWlwHJdXK/B8f4hk+NDttYH7O0dEsURjbaH53t8+EMf5vjoAM8zWSxmKGkQBE3SNOPWrTuc39pGaBLLtphOJ6RZysHJjE99+nN88jOfp6gkl69e5du+7dvxGz7z+YyN4Ro68PjBPW5/9at0vYD5eII0avfysN9hOj4mXi4IPJ1cs+hffPZJOvH/xOtPXMT1sEJn59EOrlWbEx8/ekC7vw4IhNQxXZvRyYj/7Sf+PtPRjMl4xHB9nUazycl0wtHxCVlZEaUpaVEwixNmYUicpiAU09mU5XJJFEWYpont1mPisxCYoGHRDHyWy0UN7BAOhpBsDFtooqKIIga9JhubXabjfYLAQcmCQiUoBXlRgGbUwee6jWk7pxROjZPpgngZkeZwvCy5u3tM1/dQVBTS5NmL27SDAMoSS9cJs5AoU1goTFXy9Lvew4W3vQcUlLJA+zMPQ0UNQJA6SnMJfJ/lfIxtGziNgOl8ht9ssFjOmJ4smUymCKkjpIGGyStf/gpUgla7y+37D1nb2CBXFcPNdSoMZuOIN1+/h6wyqiLl4cMdPv7JT/9/7Z3Zj2T3fd0/d1+r6tZeXb339MxwmkNyuEnUQkuWZFu2JdkPQYAgyEOQB+fJfspD1v8hBgIHNmLYSeA4gYEYCRAgEASHiSLLoihRFCkOZ5+e3pfabt19y8PtLtKMbJNmz3BRn4cZVE9PoerW6dvf3/d7vueAKvGZFz7N0c4208N9nnn+adI44t6d2xRxwvHRBFOVmPoj7m7dZ3I4oN+ps7l/wLXPf4FHpCn7S3jPJD6tU6vVCpv37tJdmMfWdSTNoKyNc0gCfus3f4ujowGO08DzpjOz6OPjYwDGkwnjyYQgDPF8bzayDIKAMCpX8Hu9Xhn4IrwdtihJEpJQYOo6nVaLLEmRxYKabSOQMRoc8uSVS1imgkBCp15lcHRInEQUZIhC2T2RFZUcAVkpHYBkQSTwfXb2B3huwCjIubvvczgKcewqpijhKBLySajkaTkTJqUFbVWXkfKIlSeeYnHjOQQEMjE/AxIza19mWYauK7RbTXYO9tFFhZs3bhGOXZIgRNHKAPVWqwUUVCoV8jyl02kxdkd0em2Ojo6wLJvrb95kf/+AqeuztrqKpimIkjCzA/O8gO3dPUzbplKvc/vmm7ROTLO73Q6TIGQwPMLWVdSioN2qk0Uuml2hs7CO+VMsCR423vOPTZlzYfB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   "source": [
    "bbox_scale = torch.tensor((w, h, w, h), dtype=torch.float32)\n",
    "ground_truth = torch.tensor([[0, 0.1, 0.08, 0.52, 0.92],\n",
    "                            [1, 0.55, 0.2, 0.9, 0.88]])\n",
    "anchors = torch.tensor([[0, 0.1, 0.2, 0.3], [0.15, 0.2, 0.4, 0.4],\n",
    "                    [0.63, 0.05, 0.88, 0.98], [0.66, 0.45, 0.8, 0.8],\n",
    "                    [0.57, 0.3, 0.92, 0.9]])\n",
    "\n",
    "fig = dl_utils.plt.imshow(img)\n",
    "show_bboxes(fig.axes, ground_truth[:, 1:] * bbox_scale, ['dog', 'cat'], 'k')\n",
    "show_bboxes(fig.axes, anchors * bbox_scale, ['0', '1', '2', '3', '4']);"
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  {
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   "metadata": {},
   "source": [
    "下面实现MultiBoxTarget函数来为锚框标注类别和偏移量。该函数将背景类别设为0，并令从零开始的目标类别的整数索引自加1（1为狗，2为猫）。"
   ]
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   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 以下函数已保存在d2lzh_pytorch包中方便以后使用\n",
    "def assign_anchor(bb, anchor, jaccard_threshold=0.5):\n",
    "    \"\"\"\n",
    "    # 按照「9.4.1. 生成多个锚框」图9.3所讲为每个anchor分配真实的bb, anchor表示成归一化(xmin, ymin, xmax, ymax).\n",
    "    https://zh.d2l.ai/chapter_computer-vision/anchor.html\n",
    "    Args:\n",
    "        bb: 真实边界框(bounding box), shape:（nb, 4）\n",
    "        anchor: 待分配的anchor, shape:（na, 4）\n",
    "        jaccard_threshold: 预先设定的阈值\n",
    "    Returns:\n",
    "        assigned_idx: shape: (na, ), 每个anchor分配的真实bb对应的索引, 若未分配任何bb则为-1\n",
    "    \"\"\"\n",
    "    na = anchor.shape[0]\n",
    "    nb = bb.shape[0]\n",
    "    jaccard = compute_jaccard(anchor, bb).detach().cpu().numpy() # shape: (na, nb)\n",
    "    assigned_idx = np.ones(na) * -1  # 初始全为-1\n",
    "    \n",
    "    # 先为每个bb分配一个anchor(不要求满足jaccard_threshold)\n",
    "    jaccard_cp = jaccard.copy()\n",
    "    for j in range(nb):\n",
    "        i = np.argmax(jaccard_cp[:, j])\n",
    "        assigned_idx[i] = j\n",
    "        jaccard_cp[i, :] = float(\"-inf\") # 赋值为负无穷, 相当于去掉这一行\n",
    "     \n",
    "    # 处理还未被分配的anchor, 要求满足jaccard_threshold\n",
    "    for i in range(na):\n",
    "        if assigned_idx[i] == -1:\n",
    "            j = np.argmax(jaccard[i, :])\n",
    "            if jaccard[i, j] >= jaccard_threshold:\n",
    "                assigned_idx[i] = j\n",
    "    \n",
    "    return torch.tensor(assigned_idx, dtype=torch.long)\n",
    "\n",
    "def xy_to_cxcy(xy):\n",
    "    \"\"\"\n",
    "    将(x_min, y_min, x_max, y_max)形式的anchor转换成(center_x, center_y, w, h)形式的.\n",
    "    https://github.com/sgrvinod/a-PyTorch-Tutorial-to-Object-Detection/blob/master/utils.py\n",
    "    Args:\n",
    "        xy: bounding boxes in boundary coordinates, a tensor of size (n_boxes, 4)\n",
    "    Returns: \n",
    "        bounding boxes in center-size coordinates, a tensor of size (n_boxes, 4)\n",
    "    \"\"\"\n",
    "    return torch.cat([(xy[:, 2:] + xy[:, :2]) / 2,  # c_x, c_y\n",
    "                      xy[:, 2:] - xy[:, :2]], 1)  # w, h\n",
    "\n",
    "def MultiBoxTarget(anchor, label):\n",
    "    \"\"\"\n",
    "    # 按照「9.4.1. 生成多个锚框」所讲的实现, anchor表示成归一化(xmin, ymin, xmax, ymax).\n",
    "    https://zh.d2l.ai/chapter_computer-vision/anchor.html\n",
    "    Args:\n",
    "        anchor: torch tensor, 输入的锚框, 一般是通过MultiBoxPrior生成, shape:（1，锚框总数，4）\n",
    "        label: 真实标签, shape为(bn, 每张图片最多的真实锚框数, 5)\n",
    "               第二维中，如果给定图片没有这么多锚框, 可以先用-1填充空白, 最后一维中的元素为[类别标签, 四个坐标值]\n",
    "    Returns:\n",
    "        列表, [bbox_offset, bbox_mask, cls_labels]\n",
    "        bbox_offset: 每个锚框的标注偏移量，形状为(bn，锚框总数*4)\n",
    "        bbox_mask: 形状同bbox_offset, 每个锚框的掩码, 一一对应上面的偏移量, 负类锚框(背景)对应的掩码均为0, 正类锚框的掩码均为1\n",
    "        cls_labels: 每个锚框的标注类别, 其中0表示为背景, 形状为(bn，锚框总数)\n",
    "    \"\"\"\n",
    "    assert len(anchor.shape) == 3 and len(label.shape) == 3\n",
    "    bn = label.shape[0]\n",
    "    \n",
    "    def MultiBoxTarget_one(anc, lab, eps=1e-6):\n",
    "        \"\"\"\n",
    "        MultiBoxTarget函数的辅助函数, 处理batch中的一个\n",
    "        Args:\n",
    "            anc: shape of (锚框总数, 4)\n",
    "            lab: shape of (真实锚框数, 5), 5代表[类别标签, 四个坐标值]\n",
    "            eps: 一个极小值, 防止log0\n",
    "        Returns:\n",
    "            offset: (锚框总数*4, )\n",
    "            bbox_mask: (锚框总数*4, ), 0代表背景, 1代表非背景\n",
    "            cls_labels: (锚框总数, 4), 0代表背景\n",
    "        \"\"\"\n",
    "        an = anc.shape[0]\n",
    "        assigned_idx = assign_anchor(lab[:, 1:], anc) # (锚框总数, )\n",
    "        bbox_mask = ((assigned_idx >= 0).float().unsqueeze(-1)).repeat(1, 4) # (锚框总数, 4)\n",
    "\n",
    "        cls_labels = torch.zeros(an, dtype=torch.long) # 0表示背景\n",
    "        assigned_bb = torch.zeros((an, 4), dtype=torch.float32) # 所有anchor对应的bb坐标\n",
    "        for i in range(an):\n",
    "            bb_idx = assigned_idx[i]\n",
    "            if bb_idx >= 0: # 即非背景\n",
    "                cls_labels[i] = lab[bb_idx, 0].long().item() + 1 # 注意要加一\n",
    "                assigned_bb[i, :] = lab[bb_idx, 1:]\n",
    "\n",
    "        center_anc = xy_to_cxcy(anc) # (center_x, center_y, w, h)\n",
    "        center_assigned_bb = xy_to_cxcy(assigned_bb)\n",
    "\n",
    "        offset_xy = 10.0 * (center_assigned_bb[:, :2] - center_anc[:, :2]) / center_anc[:, 2:]\n",
    "        offset_wh = 5.0 * torch.log(eps + center_assigned_bb[:, 2:] / center_anc[:, 2:])\n",
    "        offset = torch.cat([offset_xy, offset_wh], dim = 1) * bbox_mask # (锚框总数, 4)\n",
    "\n",
    "        return offset.view(-1), bbox_mask.view(-1), cls_labels\n",
    "    \n",
    "    batch_offset = []\n",
    "    batch_mask = []\n",
    "    batch_cls_labels = []\n",
    "    for b in range(bn):\n",
    "        offset, bbox_mask, cls_labels = MultiBoxTarget_one(anchor[0, :, :], label[b, :, :])\n",
    "        \n",
    "        batch_offset.append(offset)\n",
    "        batch_mask.append(bbox_mask)\n",
    "        batch_cls_labels.append(cls_labels)\n",
    "    \n",
    "    bbox_offset = torch.stack(batch_offset)\n",
    "    bbox_mask = torch.stack(batch_mask)\n",
    "    cls_labels = torch.stack(batch_cls_labels)\n",
    "    \n",
    "    return [bbox_offset, bbox_mask, cls_labels]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "#我们通过unsqueeze函数为锚框和真实边界框添加样本维。\n",
    "\n",
    "labels = MultiBoxTarget(anchors.unsqueeze(dim=0),\n",
    "                        ground_truth.unsqueeze(dim=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0, 1, 2, 0, 2]])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "labels[2] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[tensor([[-0.0000e+00, -0.0000e+00, -0.0000e+00, -0.0000e+00,  1.4000e+00,\n",
       "           1.0000e+01,  2.5940e+00,  7.1754e+00, -1.2000e+00,  2.6882e-01,\n",
       "           1.6824e+00, -1.5655e+00, -0.0000e+00, -0.0000e+00, -0.0000e+00,\n",
       "          -0.0000e+00, -5.7143e-01, -1.0000e+00,  4.1723e-06,  6.2582e-01]]),\n",
       " tensor([[0., 0., 0., 0., 1., 1., 1., 1., 1., 1., 1., 1., 0., 0., 0., 0., 1., 1.,\n",
       "          1., 1.]]),\n",
       " tensor([[0, 1, 2, 0, 2]])]"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "labels\n",
    "#为锚框进行标注， 类别和偏移量， 还有mask 掩码变量中的0可以在计算目标函数之前过滤掉负类的偏移量。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们根据锚框与真实边界框在图像中的位置来分析这些标注的类别。首先，在所有的“锚框—真实边界框”的配对中，锚框$A_4$与猫的真实边界框的交并比最大，因此锚框$A_4$的类别标注为猫。不考虑锚框$A_4$或猫的真实边界框，在剩余的“锚框—真实边界框”的配对中，最大交并比的配对为锚框$A_1$和狗的真实边界框，因此锚框$A_1$的类别标注为狗。接下来遍历未标注的剩余3个锚框：与锚框$A_0$交并比最大的真实边界框的类别为狗，但交并比小于阈值（默认为0.5），因此类别标注为背景；与锚框$A_2$交并比最大的真实边界框的类别为猫，且交并比大于阈值，因此类别标注为猫；与锚框$A_3$交并比最大的真实边界框的类别为猫，但交并比小于阈值，因此类别标注为背景。\n",
    "\n",
    "返回值的第二项为掩码（mask）变量，形状为(批量大小, 锚框个数的四倍)。掩码变量中的元素与每个锚框的4个偏移量一一对应。 由于我们不关心对背景的检测，有关负类的偏移量不应影响目标函数。通过按元素乘法，掩码变量中的0可以在计算目标函数之前过滤掉负类的偏移量。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0., 0., 0., 0., 1., 1., 1., 1., 1., 1., 1., 1., 0., 0., 0., 0., 1., 1.,\n",
       "         1., 1.]])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "labels[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[-0.0000e+00, -0.0000e+00, -0.0000e+00, -0.0000e+00,  1.4000e+00,\n",
       "          1.0000e+01,  2.5940e+00,  7.1754e+00, -1.2000e+00,  2.6882e-01,\n",
       "          1.6824e+00, -1.5655e+00, -0.0000e+00, -0.0000e+00, -0.0000e+00,\n",
       "         -0.0000e+00, -5.7143e-01, -1.0000e+00,  4.1723e-06,  6.2582e-01]])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "labels[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 输出预测边界框\n",
    "在模型预测阶段，我们先为图像生成多个锚框，并为这些锚框一一预测类别和偏移量。随后，我们根据锚框及其预测偏移量得到预测边界框。当锚框数量较多时，同一个目标上可能会输出较多相似的预测边界框。为了使结果更加简洁，我们可以移除相似的预测边界框。常用的方法叫作非极大值抑制（non-maximum suppression，NMS）。\n",
    "\n",
    "我们来描述一下非极大值抑制的工作原理。对于一个预测边界框$B$，模型会计算各个类别的预测概率。设其中最大的预测概率为$p$，该概率所对应的类别即$B$的预测类别。我们也将$p$称为预测边界框$B$的置信度。在同一图像上，我们将预测类别非背景的预测边界框按置信度从高到低排序，得到列表$L$。从$L$中选取置信度最高的预测边界框$B_1$作为基准，将所有与$B_1$的交并比大于某阈值的非基准预测边界框从$L$中移除。这里的阈值是预先设定的超参数。此时，$L$保留了置信度最高的预测边界框并移除了与其相似的其他预测边界框。 接下来，从$L$中选取置信度第二高的预测边界框$B_2$作为基准，将所有与$B_2$的交并比大于某阈值的非基准预测边界框从$L$中移除。重复这一过程，直到$L$中所有的预测边界框都曾作为基准。此时$L$中任意一对预测边界框的交并比都小于阈值。最终，输出列表$L$中的所有预测边界框。\n",
    "\n",
    "下面来看一个具体的例子。先构造4个锚框。简单起见，我们假设预测偏移量全是0：预测边界框即锚框。最后，我们构造每个类别的预测概率。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "anchors = torch.tensor([[0.1, 0.08, 0.52, 0.92], [0.08, 0.2, 0.56, 0.95],\n",
    "                        [0.15, 0.3, 0.62, 0.91], [0.55, 0.2, 0.9, 0.88]])\n",
    "offset_preds = torch.tensor([0.0] * (4 * len(anchors)))\n",
    "cls_probs = torch.tensor([[0., 0., 0., 0.,],  # 背景的预测概率\n",
    "                          [0.9, 0.8, 0.7, 0.1],  # 狗的预测概率\n",
    "                          [0.1, 0.2, 0.3, 0.9]])  # 猫的预测概率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 252x180 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
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     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = dl_utils.plt.imshow(img)\n",
    "show_bboxes(fig.axes, anchors * bbox_scale,\n",
    "            ['dog=0.9', 'dog=0.8', 'dog=0.7', 'cat=0.9'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "offset_preds"
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  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 以下函数已保存在d2lzh_pytorch包中方便以后使用\n",
    "from collections import namedtuple\n",
    "Pred_BB_Info = namedtuple(\"Pred_BB_Info\", [\"index\", \"class_id\", \"confidence\", \"xyxy\"])\n",
    "\n",
    "def non_max_suppression(bb_info_list, nms_threshold = 0.5):\n",
    "    \"\"\"\n",
    "    非极大抑制处理预测的边界框\n",
    "    Args:\n",
    "        bb_info_list: Pred_BB_Info的列表, 包含预测类别、置信度等信息\n",
    "        nms_threshold: 阈值\n",
    "    Returns:\n",
    "        output: Pred_BB_Info的列表, 只保留过滤后的边界框信息\n",
    "    \"\"\"\n",
    "    output = []\n",
    "    # 先根据置信度从高到低排序\n",
    "    sorted_bb_info_list = sorted(bb_info_list, key = lambda x: x.confidence, reverse=True)\n",
    "\n",
    "    while len(sorted_bb_info_list) != 0:\n",
    "        best = sorted_bb_info_list.pop(0)\n",
    "        output.append(best)\n",
    "        \n",
    "        if len(sorted_bb_info_list) == 0:\n",
    "            break\n",
    "\n",
    "        bb_xyxy = []\n",
    "        for bb in sorted_bb_info_list:\n",
    "            bb_xyxy.append(bb.xyxy)\n",
    "        \n",
    "        iou = compute_jaccard(torch.tensor([best.xyxy]), \n",
    "                              torch.tensor(bb_xyxy))[0] # shape: (len(sorted_bb_info_list), )\n",
    "        \n",
    "        n = len(sorted_bb_info_list)\n",
    "        sorted_bb_info_list = [sorted_bb_info_list[i] for i in range(n) if iou[i] <= nms_threshold]\n",
    "    return output\n",
    "\n",
    "def MultiBoxDetection(cls_prob, loc_pred, anchor, nms_threshold = 0.5):\n",
    "    \"\"\"\n",
    "    # 按照「9.4.1. 生成多个锚框」所讲的实现, anchor表示成归一化(xmin, ymin, xmax, ymax).\n",
    "    https://zh.d2l.ai/chapter_computer-vision/anchor.html\n",
    "    Args:\n",
    "        cls_prob: 经过softmax后得到的各个锚框的预测概率, shape:(bn, 预测总类别数+1, 锚框个数)\n",
    "        loc_pred: 预测的各个锚框的偏移量, shape:(bn, 锚框个数*4)\n",
    "        anchor: MultiBoxPrior输出的默认锚框, shape: (1, 锚框个数, 4)\n",
    "        nms_threshold: 非极大抑制中的阈值\n",
    "    Returns:\n",
    "        所有锚框的信息, shape: (bn, 锚框个数, 6)\n",
    "        每个锚框信息由[class_id, confidence, xmin, ymin, xmax, ymax]表示\n",
    "        class_id=-1 表示背景或在非极大值抑制中被移除了\n",
    "    \"\"\"\n",
    "    assert len(cls_prob.shape) == 3 and len(loc_pred.shape) == 2 and len(anchor.shape) == 3\n",
    "    bn = cls_prob.shape[0]\n",
    "    \n",
    "    def MultiBoxDetection_one(c_p, l_p, anc, nms_threshold = 0.5):\n",
    "        \"\"\"\n",
    "        MultiBoxDetection的辅助函数, 处理batch中的一个\n",
    "        Args:\n",
    "            c_p: (预测总类别数+1, 锚框个数)\n",
    "            l_p: (锚框个数*4, )\n",
    "            anc: (锚框个数, 4)\n",
    "            nms_threshold: 非极大抑制中的阈值\n",
    "        Return:\n",
    "            output: (锚框个数, 6)\n",
    "        \"\"\"\n",
    "        pred_bb_num = c_p.shape[1]\n",
    "        anc = (anc + l_p.view(pred_bb_num, 4)).detach().cpu().numpy() # 加上偏移量\n",
    "        \n",
    "        confidence, class_id = torch.max(c_p, 0)\n",
    "        confidence = confidence.detach().cpu().numpy()\n",
    "        class_id = class_id.detach().cpu().numpy()\n",
    "        \n",
    "        pred_bb_info = [Pred_BB_Info(\n",
    "                            index = i,\n",
    "                            class_id = class_id[i] - 1, # 正类label从0开始\n",
    "                            confidence = confidence[i],\n",
    "                            xyxy=[*anc[i]]) # xyxy是个列表\n",
    "                        for i in range(pred_bb_num)]\n",
    "        \n",
    "        # 正类的index\n",
    "        obj_bb_idx = [bb.index for bb in non_max_suppression(pred_bb_info, nms_threshold)]\n",
    "        \n",
    "        output = []\n",
    "        for bb in pred_bb_info:\n",
    "            output.append([\n",
    "                (bb.class_id if bb.index in obj_bb_idx else -1.0),\n",
    "                bb.confidence,\n",
    "                *bb.xyxy\n",
    "            ])\n",
    "            \n",
    "        return torch.tensor(output) # shape: (锚框个数, 6)\n",
    "    \n",
    "    batch_output = []\n",
    "    for b in range(bn):\n",
    "        batch_output.append(MultiBoxDetection_one(cls_prob[b], loc_pred[b], anchor[0], nms_threshold))\n",
    "    \n",
    "    return torch.stack(batch_output)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "然后我们运行MultiBoxDetection函数并设阈值为0.5。这里为输入都增加了样本维。我们看到，返回的结果的形状为(批量大小, 锚框个数, 6)。其中每一行的6个元素代表同一个预测边界框的输出信息。第一个元素是索引从0开始计数的预测类别（0为狗，1为猫），其中-1表示背景或在非极大值抑制中被移除。第二个元素是预测边界框的置信度。剩余的4个元素分别是预测边界框左上角的$x$和$y$轴坐标以及右下角的$x$和$y$轴坐标（值域在0到1之间）。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[[ 0.0000,  0.9000,  0.1000,  0.0800,  0.5200,  0.9200],\n",
       "         [-1.0000,  0.8000,  0.0800,  0.2000,  0.5600,  0.9500],\n",
       "         [-1.0000,  0.7000,  0.1500,  0.3000,  0.6200,  0.9100],\n",
       "         [ 1.0000,  0.9000,  0.5500,  0.2000,  0.9000,  0.8800]]])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output = MultiBoxDetection(\n",
    "    cls_probs.unsqueeze(dim=0), offset_preds.unsqueeze(dim=0),\n",
    "    anchors.unsqueeze(dim=0), nms_threshold=0.5)\n",
    "output"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们移除掉类别为-1的预测边界框，并可视化非极大值抑制保留的结果。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 252x180 with 1 Axes>"
      ]
     },
     "metadata": {
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     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = dl_utils.plt.imshow(img)\n",
    "for i in output[0].detach().cpu().numpy():\n",
    "    if i[0] == -1:\n",
    "        continue\n",
    "    label = ('dog=', 'cat=')[int(i[0])] + str(i[1])\n",
    "    show_bboxes(fig.axes, [torch.tensor(i[2:]) * bbox_scale], label)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "实践中，我们可以在执行非极大值抑制前**将置信度较低的预测边界框移除**，从而减小非极大值抑制的计算量。我们还可以筛选非极大值抑制的输出，例如，只保留其中置信度较高的结果作为最终输出。\n",
    "\n",
    "## 小结\n",
    "以每个像素为中心，生成多个大小和宽高比不同的锚框。\n",
    "交并比是两个边界框相交面积与相并面积之比。\n",
    "在训练集中，为每个锚框标注两类标签：一是锚框所含目标的类别；二是真实边界框相对锚框的偏移量。\n",
    "预测时，可以使用非极大值抑制来移除相似的预测边界框，从而令结果简洁。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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